NEET Physics Class 12 Chapter 7 Geometrical Optics MCQ’s

Chapter 7 Geometrical Optics Exercise 1 Multiple Choice Questions And Answers

Chapter 7 Geometrical Optics Plane Mirror

Question 1. A clock hung on a wall has marks instead of numbers on its dial. On the opposite wall there is a mirror, and the image of the clock in the mirror if read, indicates the time as 8: 20. What is the time on the clock

1. 3: 40
2. 4: 40
3. 5: 20
4. 4: 20

Answer: 1. 3: 40

Question 2. A ray of light incident on a plane mirror at an angle of incidence of 30°. The deviation produced by the mirror is

1. 30°
2. 60°
3. 90°
4. 120°

Answer: 4. 120°

Question 3. The image of a real object formed by a plane mirror is

1. Erect, real, and of equal size
2. Erect, virtual, and of equal size
3. Inverted, real, and of equal size
4. Inverted, virtual, and of equal size

Answer: 2. Erect, virtual, and of equal size

Question 4. Two mirrors are inclined at an angle θ as shown in the figure. A light ray is incident parallel to one of the mirrors. Light will start retracing its path after the third reflection if :

1. θ = 45
2. θ = 30
3. θ= 60
4. All three

Answer: 2. θ = 30

Question 5. If an object is placed symmetrically between two plane mirrors, inclined at an angle of 72°, then the total number of images formed is

1. 5
2. 4
3. 2
4. Infinite

Answer: 2. 4

Question 6. A man 180 cm high stands in front of a plane mirror. His eyes are at a height of 170 cm from the floor. Then the minimum length of the plane mirror for him to see his full-length image is

1. 90 cm
2. 180 cm
3. 45 cm
4. 360 cm

Answer: 1. 90 cm

Question 7. A thick plane mirror shows a number of images of the filament of an electric bulb. Of these, the brightest image is the

1. First
2. Second
3. Last
4. Fourth

Answer: 2. Second

Question 8. Two vertical plane mirrors are inclined at an angle of 60° with each other. A ray of light traveling horizontally is reflected first from one mirror and then from the other. The resultant deviation is

1. 60°
2. 100°
3. 180°
4. 240°

Answer: 4. 240°

Question 9. When a plane mirror is placed horizontally on level ground at a distance of 60m from the foot of a tower, the top of the tower and its image in the mirror subtend an angle of 90° at the eye. The height of the tower will be

1. 30 m
2. 60 m
3. 90 m
4. 120 m

Answer: 2. 60 m

Question 10. An object is at a distance of 0.5 m in front of a plane mirror. The distance between the object and the image is

1. 0.5 m
2. 1 m
3. 0.25 m
4. 1.5 m

Answer: 2. 1 m

Question 11. The light reflected by a plane mirror may form a real image

1. If the ray incident on the mirror is diverging
2. If the rays incident on the mirror are converging
3. If the object is placed very close to the mirror
4. Under no circumstances

Answer: 2. If the rays incident on the mirror are converging

Question 12. Two plane mirrors are inclined to each other at an angle of 600. If a ray of light incident on the first mirror is parallel to the second mirror, it is reflected from the second mirror

1. Perpendicular to the first mirror
2. Parallel to the first mirror
3. Parallel to the second mirror
4. Perpendicular to the second mirror

Answer: 2. Parallel to the first mirror

Question 13. It is desired to photograph the image of an object placed at a distance of 3 m from a plane mirror. The camera, which is at a distance of 4.5 m from the mirror should be focused for a distance of

1. 3 m
2. 4.5 m
3. 6 m
4. 7.5 m

Answer: 4. 7.5 m

Question 14. An unnumbered wall clock shows time 04: 25: 37, where 1st term represents hours, 2nd represents minutes and the last term represents seconds. What time will its image in a plane mirror show?

1. 08: 35: 23
2. 07: 35: 23
3. 07: 34: 23
4. None of these

Answer: 3. 07: 34: 23

Question 15. Two plane mirrors are parallel to each other and spaced 20 cm apart. An object is kept in between them at 15 cm from A. Out of the following at which point(s) image(s) is/are not formed in mirror A (distance measured from mirror A):

1. 15 cm
2. 25 cm
3. 45 cm
4. 55 cm

Answer: 3. 45 cm

Question 16. A thick mirror produces a number of images of an object. The brightest images are

1. First
2. Second
3. Third
4. Last one

Answer: 2. Second

Question 17. If two mirrors are kept at 60° from each other, then the number of images formed by them is

1. 5
2. 6
3. 7
4. 8

Answer: 1. 5

Question 18. To get three images of a single object, one should have two plane mirrors at an angle of

1. 60°
2. 90°
3. 120°
4. 30°

Answer: 2. 90°

Question 19. A man is 6 feet tall. In order to see his entire image, he requires a plane mirror of minimum length equal to:

1. 6 ft
2. 12 ft
3. 2 ft
4. 3 ft

Answer: 4. 3 ft

Chapter 7 Geometrical Optics Spherical Mirror

Question 1. A convex mirror has a focal length of f. A real object is placed at a distance f in front of it from the pole, then it produces an image at

1. Infinity
2. f
3. f/2
4. 2f

Answer: 3. f/2

Question 2. The image formed by the convex mirror of a focal length 30 cm is a quarter of the size of the object. Then the distance of the object from the mirror is-

1. 30 cm
2. 90 cm
3. 120 cm
4. 60 cm

Answer: 2. 90 cm

Question 3. The largest distance of the image of a real object from a convex mirror of focal length 10 cm can be

1. 20 cm
2. Infinite
3. 10 cm
4. Depends on the position of the object

Answer: 3. 10 cm

Question 4. In the case of the concave mirror, the minimum distance between a real object and its real image is

1. f
2. 2f
3. 4f
4. Zero

Answer: 4. Zero

Question 5. A luminous point object is moving along the principal axis of a concave mirror of focal length 12 cm towards it. When its distance from the mirror is 20 cm its velocity is 4 cm/s. The velocity of the image in cm/s at that instant is

1. 6, towards the mirror
2. 6, away from the mirror
3. 9, away from the mirror
4. 9, towards the mirror.

Answer: 3. 9, away from the mirror

Question 6. Which of the following can form an erect, virtual, diminished image?

1. Plane mirror
2. Concave mirror
3. Convex mirror
4. None of these

Answer: 3. Convex mirror

Question 7. The focal length of a concave mirror is 20 cm. Determine where an object must be placed to form an image magnified two times when the image is real

1. 30cm from the mirror
2. 10cm from the mirror
3. 20cm from the mirror
4. 15cm from the mirror

Answer: 1. 30cm from the mirror

Question 8. A convex mirror of focal length f forms an image that is 1/n times the object. The distance of the object from the mirror is

1. (n-1) f
2. \(\left(\frac{n-1}{n}\right) f\)
3. \(\left(\frac{n+1}{n}\right) f\)
4. (n+1) f

Answer: 1. (n-1) f

Question 9. Which of the following could not produce a virtual image

1. Plane mirror
2. Convex mirror
3. Concave mirror
4. All the above can produce a virtual image

Answer: 4. All the above can produce a virtual image

Question 10. The field of view is maximum for

1. Plane mirror
2. Concave mirror
3. Convex mirror
4. Cylindrical mirror

Answer: 3. Convex mirror

Question 11. The focal length of a concave mirror is f and the distance from the object to the principal focus is x. The ratio of the size of the image to the size of the object is

1. \(\frac{f+x}{f}\)
2. \(\frac{f}{x}\)
3. \(\sqrt{\frac{f}{x}}\)
4. \(\frac{f^2}{x^2}\)

Answer: 2. \(\frac{f}{x}\)

Question 12. The image formed by a convex mirror is

1. Virtual
2. Real
3. Enlarged
4. Inverted

Answer: 1. Virtual

Question 13. The image formed by a convex mirror of a focal length of 30 cm is a quarter of the size of the object. The distance of the object from the mirror is

1. 30 cm
2. 90 cm
3. 120 cm
4. 60 cm

Answer: 2. 90 cm

Question 14. A person sees his virtual image by holding a mirror very close to the face. When he moves the mirror away from his face, the image becomes inverted. What type of mirror he is using

1. Plane mirror
2. Convex mirror
3. Concave mirror
4. None of these

Answer: 3. Concave mirror

Question 15. A square ABCD of side 1mm is kept at a distance of 15 cm in front of the concave mirror as shown in the figure. The focal length of the mirror is 10 cm. The length of the perimeter of its image will be(nearly):

1. 8 mm
2. 2 mm
3. 12 mm
4. 6 mm

Answer: 3. 12 mm

Question 16. A particle is moving towards a fixed spherical mirror. The image:

1. Must move away from the mirror
2. Must move towards the mirror
3. May move towards the mirror
4. Will move towards the mirror, only if the mirror is convex.

Answer: 3. May move towards the mirror

Question 17. The distance of an object from the focus of a convex mirror of radius of curvature ‘a’ is ‘b’. Then the distance of the image from the focus is:

1. b²/ 4a
2. a / b²
3. a²/ 4b
4. 4b / a²

Answer: 3. a² / 4b

Question 18. An object is placed at a distance u from a concave mirror and its real image is received on a screen placed at a distance of v from the mirror. If f is the focal length of the mirror, then the graph between 1/v versus 1/u is

Answer: 2

Chapter 7 Geometrical Optics Refraction In General, Refraction At Plane Surface And Total Internal Reflection

Question 1. Total internal reflection occurs in waves when a wave enters-

1. Glass from air
2. Air from vacuum
3. Water from air
4. Air from water

Answer: 4. Air from water

Question 2. An object is placed at a 24 cm distance above the surface of a lake. If water has a refractive index of 4/3, then at what distance from the lake surface, a fish will sight the object

1. 32 cm above the surface of the water
2. 18 cm over the surface of the water
3. 6 cm over the surface of the water
4. 6 cm below the surface of the water

Answer: 1. 32 cm above the surface of water

Question 3. The time taken to cross a 4 mm window glass with a refractive index of 1.5 will be

1. 2 x 10^-8 sec
2. 2 x 10⁸ sec
3. 2 x 10^-11 sec
4. 2 x 10¹¹ sec

Answer: 3. 2 x 10^-11 sec

Question 4. The total internal reflection of a beam of light occurs when a beam of light enters- [i_c = critical angle, i = angle of incidence]

1. Rarer medium from a denser one and i < i_c
2. Rarer medium from a denser i > i_c
3. Denser medium from rarer i < i_c
4. Denser medium from a rarer i > i_c

Answer: 2. Rarer medium from a denser i > i_c

Question 5. A bubble in the glass slab [μ = 1.5] when viewed from one side appears at 5 cm and at 2 cm from another side the thickness of the slab is

1. 3.75 cm
2. 23 cm
3. 10.5 cm
4. 1.5 cm

Answer: 3. 10.5 cm

Question 6. A light wave travels from glass to water. The refractive index for glass and water are and — respectively. The value of the critical angle will be:

1. \(\sin ^{-1}\left(\frac{1}{2}\right)\)
2. \(\sin ^{-1}\left(\frac{9}{8}\right)\)
3. \(\sin ^{-1}\left(\frac{8}{9}\right)\)
4. \(\sin ^{-1}\left(\frac{5}{7}\right)\)

Answer: 3. \(\sin ^{-1}\left(\frac{8}{9}\right)\)

Question 7. The wavelength of light in a vacuum is 6000 Å and in a medium, it is 4000 Å. The refractive index of the medium is:

1. 2.4
2. 1.5
3. 1.2
4. 0.67

Answer: 2. 1.5

Question 8. A beam of light is converging towards a point. A plane parallel plate of glass of thickness t, the refractive index μ is introduced in the path of the beam. The convergent point is shifted by (assume near normal incidence):

1. \(t\left(1-\frac{1}{\mu}\right)\) away
2. \(t\left(1+\frac{1}{\mu}\right)\) away
3. \(t\left(1-\frac{1}{\mu}\right)\) nearer
4. \(t\left(1+\frac{1}{\mu}\right)\) nearer

Answer: 1. \(t\left(1-\frac{1}{\mu}\right)\) away

Question 9. When a beam of light goes from a denser medium (μ_d) to a rarer medium (μ_r), then it is generally observed that the magnitude of the angle of incidence is half that of the angle of refraction. Then magnitude of incident angle will be- (here μ = μ_d/μ_c)

1. \(2 \sin ^{-1}\left(\frac{\mu}{2}\right)\)
2. \(2 \cos ^{-1} \mu\)
3. \(\cos ^{-1}\left(\frac{\mu}{2}\right)\)
4. \(2 \cos ^{-1}\left(\frac{\mu}{2}\right)\)

Answer: 2. \(2 \cos ^{-1} \mu\)

Question 10. To an observer on the earth, the stars appear to twinkle. This can be ascribed to

1. The fact that stars do not emit light continuously
2. Frequent absorption of starlight by their own atmosphere
3. Frequent absorption of starlight by the Earth’s atmosphere
4. The refractive index fluctuations in the Earth’s atmosphere

Answer: 4. The refractive index fluctuations in the earth’s atmosphere

Question 11. The refractive index of a certain glass is 1.5 for light whose wavelength in vacuum is 6000 Å. The wavelength of this light, when it passes through glass, is

1. 4000 Å
2. 6000 Å
3. 9000 Å
4. 15000 Å

Answer: 1. 4000 Å

Question 12. When light travels from one medium to the other of which the refractive index is different, then which of the following will change

1. Frequency, wavelength, and velocity
2. Frequency and wavelength
3. Frequency and velocity
4. Wavelength and velocity

Answer: 4. Wavelength and velocity

Question 13. A monochromatic beam of light passes from a denser medium into a rarer medium. As a result

1. Its velocity increases
2. Its velocity decreases
3. Its frequency decreases
4. Its wavelength decreases

Answer: 1. Its velocity increases

Question 14. A rectangular tank of depth 8 meters is full of water (μ = 4/3), the bottom is seen at the depth

1. 6m
2. 8/3 m
3. 8 cm
4. 10 cm

Answer: 1. 6m

Question 15. If _iμ_j represents the refractive index when a light ray goes from medium i to medium j, then the product ₂μ₁ X ₃μ₂ X ₄μ₃ is equal to

1. \({ }_3 \mu_1\)
2. \({ }_3 \mu_2\)
3. \(\frac{1}{{ }_1 \mu_4}\)
4. \({ }_4 \mu_2\)

Answer: 3. \(\frac{1}{{ }_1 \mu_4}\)

Question 16. The wavelength of light diminishes μ times (μ = 1.33 for water) in a medium. A driver from inside the water looks at an object whose natural color is green. He sees the object as

1. Green
2. Blue
3. Yellow
4. Red

Answer: 1. Green

Question 17. A diver in a swimming pool wants to signal his distress to a person lying on the edge of the pool by flashing his waterproof flashlight

1. He must direct the beam vertically upwards
2. He has to direct the beam horizontally
3. He has to direct the beam at an angle to the vertical which is slightly less than the critical angle of incidence for total internal reflection
4. He has to direct the beam at an angle to the vertical which is slightly more than the critical angle of incidence for the total internal reflection

Answer: 3. He has to direct the beam at an angle to the vertical which is slightly less than the critical angle of incidence for total internal reflection

Question 18. The wavelength of light in two liquids ‘x’ and ‘y’ is 3500 Å and 7000 Å, then the critical angle of x relative to y will be

1. 60°
2. 45°
3. 30°
4. 15°

Answer: 3. 30°

Question 19. Total internal reflection of a ray of light is possible when the (i_c = critical angle, i = angle of incidence)

1. Ray goes from denser medium to rarer medium and i < i_c
2. Ray goes from denser medium to rarer medium and i > i_c
3. Ray goes from rarer medium to denser medium and i > i_c
4. Ray goes from rarer medium to denser medium and i < i_c

Answer: 2. Ray goes from denser medium to rarer medium and i > i_c

Question 20. A diver at a depth of 12 m in water (μ = 4/3) sees the sky in a cone of semi-vertical angle

1. sin^-1(4/3)
2. tan^-1(4/3)
3. sin^-1(3/4)
4. 90°

Answer: 3. sin^-1(3/4)

Question 21. The critical angle for a diamond (refractive index = 2) is

1. About 20°
2. 60°
3. 45°
4. 30°

Answer: 4. 30°

Question 22. The reason for the shining of air bubbles in water is

1. Diffraction of light
2. Dispersion of light
3. Scattering of light
4. Total internal reflection of light

Answer: 4. Total internal reflection of light

Question 23. ‘Mirage’ is a phenomenon due to

1. Reflection of light
2. Refraction of light
3. Total internal reflection of light
4. Diffraction of light

Answer: 3. Total internal reflection of light

Question 24. Given that the velocity of light in quartz =1.5 x 10⁸ m/s and the velocity of light in glycerine = (9/4) x 10⁸ m/s. Now a slab made of quartz is placed in glycerine as shown. The shift of the object produced by the slab is

1. 6 cm
2. 3.55 cm
3. 9 cm
4. 2 cm

Answer: 1. 6 cm

Question 25. A ray of light passes from a vacuum into a medium of refractive index n. If the angle of incidence is twice the angle of refraction, then the angle of incidence is:

1. cos^-1 (n/2)
2. sin^-1 (n/2)
3. 2 cos^-1 (n/2)
4. 2 sin^-1 (n/2)

Answer: 3. 2 cos^-1 (n/2)

Question 26. The critical angle of light going from medium A to medium B is θ. The speed of light in medium A is v. The speed of light in medium B is:

1. \(\frac{v}{\sin \theta}\)
2. \(v \sin \theta\)
3. \(v \cot \theta\)
4. \(v \tan \theta[latex]

Answer: 1. [latex]\frac{v}{\sin \theta}\)

Question 27. A ray of light passes through four transparent media with refractive indices μ₁, μ₂, μ_3, and μ₄ as shown in the figure. The surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB, we must have:

1. μ₁ = μ₂
2. μ₂ = μ₃
3. μ₃ = μ₄
4. μ₄ = μ₁

Answer: 4. μ₄ = μ₁

Question 28. If the critical angle for total internal reflection from a medium to vacuum is 30°, then the speed of light in the medium is

1. 6 x 10⁸ m/s
2. 3 x 10⁸ m/s
3. 2 x 10⁸ m/s
4. 1.5 x 10⁸ m/s

Answer: 4. 1.5 x 10⁸ m/s

Question 29. If a glass rod is immersed in a liquid of the same refractive index, then it will appear

1. Bent
2. Longer
3. Shorter
4. Invisible

Answer: 4. Invisible

Question 30. A metal coin is at the bottom of a beaker filled with a liquid of refractive index 4/3 to a height of 6 cm. To an observer looking from above the surface of the liquid, the coin will appear at a depth of :

1. 7.5 cm
2. 6.75 cm
3. 4.5 cm
4. 1.5 cm

Answer: 3. 4.5 cm

Question 31. A transparent cube with a 15 cm edge contains a small air bubble. Its apparent depth when viewed through one face is 6 cm and when viewed through the opposite face is 4 cm. Then the refractive index of the material of the cube is

1. 2.0
2. 2.5
3. 1.6
4. 1.5

Answer: 4. 1.5

Question 32. If the critical angle for total internal reflection from a medium to vacuum is 30°, the velocity of light in a medium is

1. 3 x 10⁸ m/s
2. 1.5 x 10⁸ m/s
3. 6 x 10⁸ m/s
4. 10⁸ m/s

Answer: 2. 1.5 x 10⁸ m/s

Question 33. For the given incident ray as shown in the figure, the condition of the total internal reflection of the ray will be satisfied if the refractive index of the block is:

1. \(n>\frac{\sqrt{3}+1}{2}\)
2. \(n<\frac{\sqrt{3}+1}{2}\)
3. \(n>\sqrt{\frac{3}{2}}\)
4. \(n<\sqrt{\frac{3}{2}}\)

Answer: 3. \(n>\sqrt{\frac{3}{2}}\)

Question 34. A small coin is resting on the bottom of a beaker filled with a liquid. A ray of light from the coin travels up to the surface of the liquid and moves along its surface How fast is the light traveling in the liquid?

1. 1.8 × 10⁸ m/s
2. 2.4 × 10⁸ m/s
3. 3.0 × 10⁸ m/s
4. 1.2 × 10⁸ m/s

Answer: 1. 1.8 × 10⁸ m/s

Question 35. Which of the following is used in optical fibers?

1. Total internal reflection
2. Scattering
3. Diffraction
4. Refraction

Answer: 1. Total internal reflection

Question 36. Transmission of light in optical fiber is due to the:

1. Scattering
2. Diffraction
3. Polarisation
4. Multiple total internal reflections

Answer: 4. Multiple total internal reflections

Question 37. Which of the following will remain constant in the phenomenon of refraction of light?

1. Wavelength
2. Velocity
3. Frequency
4. None

Answer: 3. Frequency

Question 38. The phenomena of total internal reflection are seen when the angle of incidence is:

1. 90°
2. Greater than the critical angle
3. Equal to the critical angle
4. 0°

Answer: 2. Greater than critical angle

Question 39. A ray of light from a denser medium strikes a rarer medium of an angle of incidence i. the reflected and refracted rays make an angle of 900 with each other. The angle of reflection and refraction are r and r’. The critical angle is

1. sin^-1 [tan r]
2. sin^-1 [cot i]
3. sin^-1 [tan r’]
4. sin^-1 [sin r’]

Answer: 1. sin^-1 [cot i]

Question 40. A ray of light travels from an optically denser to a rarer medium. The critical angle for the two media is c. The maximum possible deviation of the ray will be–

1. 2c
2. π/2 – c
3. π – c
4. π – 2c

Answer: 2. π/2 – c

Question 41. A ray of light traveling in water is incident on its surface open to air. The angle of incidence is θ, which is less than the critical angle. Then there will be :

1. Only a reflected ray and no refracted ray
2. Only a refracted ray and no reflected ray
3. A reflected ray and a refracted ray and the angle between them would be less than 180° – 2θ
4. A reflected ray and a refracted ray and the angle between them would be greater than 180° – 2θ.

Answer: 3. A reflected ray and a refracted ray and the angle between them would be less than 180° – 2θ

Question 42. A light beam is traveling from Region 1 to Region 4. The refractive index in Regions 1, 2, 3, and 4 are n₀, and, respectively. The angle of incidence θ for which the beam just misses entering Region 4 is

1. \(\sin ^{-1}\left(\frac{3}{4}\right)\)
2. \(\sin ^{-1}\left(\frac{1}{8}\right)\)
3. \(\sin ^{-1}\left(\frac{1}{4}\right)\)
4. \(\sin ^{-1}\left(\frac{1}{3}\right)\)

Answer: 2. \(\sin ^{-1}\left(\frac{1}{8}\right)\)

Question 43. The wavelength of light in two liquids x and y are 3500 Å and 7000 Å, then the critical angle of x relative to y will be

1. 60°
2. 45°
3. 30°
4. 15°

Answer: 3. 30°

Question 44. The correct thickness of glass having _aμ_g = 1.5, which permits an equal number of wavelengths as that of an 18 cm long column of water is- [_aμ_g = 4/3]

1. 12 cm
2. 16 cm
3. 18 cm
4. 24 cm

Answer: 2. 16 cm

Question 45. Dimension of \(\frac{1}{\mu_0 \varepsilon_0}\) is (where symbols have usual meaning):

1. [LT^-1]
2. [L^-1T]
3. [L^-2T]
4. [L²T^-2]

Answer: 4. [L²T^-2]

Question 46. When a ray of light is reflected from a denser medium interface, then the following changes

1. Wavelength
2. Phase
3. Frequency
4. Speed

Answer: 2. Phase

Question 47. If the refractive index of a medium is 1.5, then the velocity of light in that medium will be:

1. 10 x 10⁸
2. 2 x 10⁸
3. 3 x 10⁸
4. 4 x 10⁸

Answer: 2. 2 x 10⁸

Question 48. Light enters into glass from the air then it:

1. Frequency increases
2. Frequency decreases
3. Wavelength increases
4. Wavelength decreases

Answer: 4. Wavelength decreases

Question 49. The value of the refractive index for any medium is

1. \(1 / \sqrt{\mu_r \varepsilon_r}\)
2. \(\sqrt{\mu_{\mathrm{r}} \varepsilon_{\mathrm{r}}}\)
3. \(\sqrt{\mu_{\mathrm{r}} / \varepsilon_{\mathrm{r}}}\)
4. \(\sqrt{\varepsilon_{\mathrm{r}} / \mu_{\mathrm{r}}}\)

Answer: 2. \(\sqrt{\mu_{\mathrm{r}} \varepsilon_{\mathrm{r}}}\)

Chapter 7 Geometrical Optics Refraction By Prism

Question 1. A ray of light is incident normally on one of the faces of a prism apex angle of 30° and refractive index √2. The angle of deviation of the ray is:

1. 15°
2. 22.5°
3. 0°
4. 12.5°

Answer: 1. 15°

Question 2. The refractive index of the material of the prism of 60º angle is √2. At what angle the ray of light be incident on it so that minimum deviation takes place?

1. 45º
2. 60º
3. 30º
4. 75º

Answer: 1. 45º

Question 3. A ray of light is incident at an angle of 60° on one face of a prism which has an apex angle of 30°. The ray emerging out of the prism makes an angle of 30° with the incident ray. The refractive index of the material of the prism is

1. √2
2. √3
3. 1.5
4. 1.6

Answer: 2. √3

Question 4. If the critical angle for the medium of the prism is C and the angle of the prism is A, then there will be no emergent ray when

1. A < 2C
2. A = 2C
3. A > 2C
4. A ≥ 2C

Answer: 3. A > 2C

Question 5. A ray of monochromatic light is incident on one refracting face of a prism of angle 75°. It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is √2, the angle of incidence on the first face of the prism is

1. 30°
2. 45°
3. 60°
4. 0°

Answer: 2. 45°

Question 6. A ray of light is incident at an angle i on a surface of a prism of small angle A and emerges normally from the opposite surface. If the refractive index of the material of the prism is μ, the angle of incidence i is nearly equal to:

1. A/μ
2. A/(2 μ)
3. μ A
4. μ A/2

Answer: 3. μ A

Question 7. A prism having an apex angle of 4° and a refractive index of 1.50 is located in front of a vertical plane mirror as shown. A horizontal ray of light is incident on the prism. The total angle through which the ray is deviated is:

1. 4° clockwise
2. 178° clockwise
3. 2° clockwise
4. 8° clockwise

Answer: 2. 178° clockwise

Question 8. The critical angle between an equilateral prism and air is 45°. If the incident ray is perpendicular to the refracting surface, then

1. After deviation, it will emerge from the second refracting surface
2. It is totally reflected on the second surface and emerges perpendicularly from the third surface in air
3. It is totally reflected from the second and third refracting surfaces and finally emerges from the first surface
4. It is totally reflected from all three sides of the prism and never emerges out

Answer: 2. It is totally reflected on the second surface and emerges out perpendicularly from the third surface in the air

Question 9. When light rays are incident on a prism at an angle of 45°, the minimum deviation is obtained. If the refractive index of the material of the prism is √2, then the angle of the prism will be

1. 30°
2. 40°
3. 50°
4. 60°

Answer: 4. 60°

Question 10. The refractive index of a prism for a monochromatic wave is √2 and its refracting angle is 60°. For minimum deviation, the angle of incidence will be

1. 30°
2. 45°
3. 60°
4. 75°

Answer: 2. 45°

Question 11. A parallel beam of monochromatic light is incident at one surface of an equilateral prism. The angle of incidence is 55° and the angle of emergence is 46°. The angle of minimum deviation will be

1. Less than 41°
2. Equal to 41°
3. More than 41°
4. None of the above

Answer: 1. Less than 41°

Question 12. The minimum refractive index of a material, of a prism of apex angle 90°, for which light cannot be transmitted for any value of i:

1. √3
2. 1.5
3. √2
4. None of these

Answer: 3. √2

Question 13. A horizontal light ray passes through a prism (μ = 1.5) of angle 4°. Further, it is incident on a plane mirror M that has been placed vertically. By what angle the mirror is rotated so that the ray after reflection becomes horizontal?

1. 1°
2. 2°
3. 4°
4. 8°

Answer: 1. 1°

Question 14. For a prism of refractive index √3, the angle of the prism is equal to the angle of minimum deviation. The value of the angle of the prism is

1. 60°
2. 50°
3. 45°
4. 30°

Answer: 1. 60°

Question 15. An equilateral prism is kept on a horizontal surface. A typical ray of light PQRS is shown in the figure. For minimum deviation

1. The ray PQ must be horizontal
2. The ray RS must be horizontal
3. The ray QR must be horizontal
4. Any one of them can be horizontal

Answer: 3. The ray QR must be horizontal

Question 16. A prism has a refracting angle of 60°. If it produces a minimum deviation of 30° in an incident ray, the angle of incidence is

1. 15°
2. 30°
3. 45°
4. 60°

Answer: 3. 45°

Question 17. A thin prism P of angle 4° made of glass of refractive index 1.54 is combined with a thin prism Q made of glass of refractive index 1.72 to produce dispersion without deviation. The angle of prism Q is:

1. 4°
2. 3°
3. 2.6°
4. 5.3°

Answer: 2. 3°

Question 18. A prism has a refracting angle of 60°. A ray of given monochromatic light suffers a minimum deviation of 38° in passing through the prism refractive index of the material of the prism is:

1. 1.5094
2. 1.3056
3. 0.7849
4. 2.425

Answer: 1. 1.5094

Question 19. An equilateral prism has p = √3. Its angle of minimum deviation will be:

1. 30°
2. 60°
3. 120°
4. 45°

Answer: 2. 60°

Question 20. The deviation is maximum for which color?

1. violet
2. Red
3. Blue
4. Green

Answer: 1. violet

Question 21. The refractive indices of violet and red light are 1.54 and 1.52 respectively. If the angle of the prism is 10°, the angular dispersion is

1. 0.02°
2. 0.2°
3. 3.06°
4. 30.6°

Answer: 2. 0.2°

Question 22. A microscope is focused on a mark on a piece of paper and then a slab of glass of thickness 3 cm and refractive index 1.5 is placed over the mark. How should the microscope be moved to get the mark in focus again?

1. 1 cm upward
2. 4.5 cm downward
3. 1 cm downward
4. 2 cm upward

Answer: 1. 1 cm upward

Question 23. The refractive index of glass is 1.520 for red light and 1.525 for blue light. Let D₁, and D₂ be angles of minimum deviation for red and blue light respectively in a prism of this glass. Then,

1. D₁ can be less than or greater than D₂ depending on the angle of the prism
2. D₁ > D₂
3. D₁ < D₂
4. D₁ = D₂

Answer: 3. D₁ = D₂

Question 24. A light ray is incident perpendicularly to one face to a 90º prism and is totally internally reflected at the glass-air interface. If the angle of reflection is 45º, we conclude that the refractive index n is

1. \(\mathrm{n}<\frac{1}{\sqrt{2}}\)
2. \(n>\sqrt{2}\)
3. \(n>\frac{1}{\sqrt{2}}\)
4. \(n<\sqrt{2}\)

Answer: 2. \(n>\sqrt{2}\)

Chapter 7 Geometrical Optics Refraction By Spherical Surface

Question 1. An object is placed at a distance of 20 cm, in a rarer medium, from the pole of a convex spherical refracting surface of a radius of curvature 10 cm. If the refractive index of the rarer medium is 1 and of the refracting medium is 2, then the position of the image is at

1. (40/3) cm from the pole and inside the denser medium
2. 40 cm from the pole and inside the denser medium.
3. (40/3) cm from the pole and outside the denser medium
4. 40 cm from the pole and outside the denser medium.

Answer: 2. 40 cm from the pole and inside the denser medium.

Question 2. There is a small black dot at the center C of a solid glass sphere of refractive index μ. When seen from outside, the dot will appear to be located:

1. Away from C for all values of μ
2. At C for all values of μ
3. At C for μ = 1.5, but away from C for μ ≠ 1.5
4. At C only for ≤ μ ≤ 1.5.

Answer: 2. At C for all values of μ

Question 3. The image for the converging beam after refraction through the curved surface is formed at:

1. \(x=40 \mathrm{~cm}\)
2. \(x=\mathrm{cm}\)
3. \(x=\frac{40}{3}-\frac{40}{3} \mathrm{~cm}\)
4. \(x=\frac{180}{7} \mathrm{~cm}\)

Answer: 1. \(x=40 \mathrm{~cm}\)

Question 4. In the figure shown a point object O is placed in air. A spherical boundary of radius of curvature 1.0 m separates two media. AB is the principal axis. The refractive index above AB is 1.6 and below AB is 2.0. The separation between the images formed due to refraction at the spherical surface is:

1. 12 m
2. 20 m
3. 14 m
4. 10 m

Answer: 1. 12 m

Chapter 7 Geometrical Optics Lens

Question 1. A convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens. Then its focal length will

1. Become zero
2. Become infinite
3. Become small, but non-zero
4. Remain unchanged

Answer: 2. Become infinite

Question 2. A biconvex lens with equal radii of curvature has a refractive index of 1.6 and a focal length of 10 cm. Its radius of curvature will be:

1. 20 cm
2. 16 cm
3. 10 cm
4. 12 cm

Answer: 4. 12 cm

Question 3. A convex lens forms a real image 9 cm long (high) on a screen. Without altering the position of the object and the screen, the lens is displaced and we get again a real image 4 cm long (high) on the screen. Then the length of the object is

1. 9 cm
2. 4 cm
3. 6 cm
4. 36 cm

Answer: 3. 6 cm

Question 4. An object is placed at a distance of 5 cm from a convex lens of focal length 10 cm, then the image is

1. Real, diminished, and at a distance of 10 cm from the lens.
2. Real, enlarged, and at a distance of 10 cm from the lens.
3. Virtual, enlarged, and at a distance of 10 cm from the lens.
4. Virtual, diminished, and at a distance of 10/3 cm from the lens.

Answer: 3. Virtual, enlarged, and at a distance of 10 cm from the lens.

Question 5. Inside water, an air bubble behaves-

1. Always like a convex lens
2. Always like a concave lens
3. Always like a slab of equal thickness
4. Sometimes concave and sometimes like a convex lens

Answer: 2. Always like a concave lens

Question 6. A lens behaves as a converging lens in air and a diverging lens in water. The refractive index of the material is (refractive index of water = 1.33)

1. Equal to unity
2. Equal to 1.33
3. Between unity and 1.33
4. Greater than 1.33

Answer: 3. Between unity and 1.33

Question 7. In the figure given below, there are two convex lenses L₁ and L₂ having focal lengths of f₁ and f₂ respectively. The distance between L₁ and L₂ will be

1. f₁
2. f₂
3. f₁ + f₂
4. f₁-f₂

Answer: 3. f₁ + f₂

Question 8. A virtual erect image by a diverging lens is represented by (u, v, f are coordinates)

Answer: 4

Question 9. What should be the value of distance d so that the final image is formed on the object itself? (focal lengths of the lenses are written on the lenses).

1. 10 cm
2. 20 cm
3. 5 cm
4. None of these

Answer: 1. 10 cm

Question 10. A thin linear object of size 1 mm is kept along the principal axis of a convex lens of focal length 10 cm. The object is 15 cm from the lens. The length of the image is:

1. 1 mm
2. 4 mm
3. 2 mm
4. 8 mm

Answer: 2. 4 mm

Question 11. A glass lens is placed in a medium in which it is found to behave like a glass plate. The refractive index of the medium will be:

1. Greater than the refractive index of glass
2. Smaller than the refractive index of glass
3. Equal to the refractive index of glass
4. No case will be possible from the above

Answer: 3. Equal to the refractive index of glass

Question 12. A divergent lens will produce

• Always a virtual image
• Always real image
• Sometimes real and sometimes virtual
• None of above

Answer: 1. Always a virtual image

Question 13. The minimum distance between an object and its real image formed by a convex lens is

1. 1.5 f
2. 2 f
3. 2.5 f
4. 4 f

Answer: 4. 4 f

Question 14. A biconvex lens forms a real image of an object placed perpendicular to its principal axis. Suppose the radii of curvature of the lens tend to infinity. Then the image would

1. Disappear
2. Remain as real image still
3. Be virtual and of the same size as the object
4. Suffer from aberrations

Answer: 3. Suffer from aberrations

Question 15. The radius of curvature of the convex surface of a thin plano-convex lens is 15 cm and the refractive index of its material is 1.6. The power of the lens will be

1. +1D
2. -2D
3. +3D
4. +4D

Answer: 4. +4D

Question 16. A lens is placed between a source of light and a wall. It forms images of areas A₁ and A₂ on the wall for its two different positions. The area of the source of light is

1. \(\frac{A_1+A_2}{2}\)
2. \(\left[\frac{1}{A_1}+\frac{1}{A_2}\right]^{-1}\)
3. \(\sqrt{A_1 A_2}\)
4. \(\left[\frac{\sqrt{A_1}+\sqrt{A_2}}{2}\right]^2\)

Answer: 3. \(\left[\frac{\sqrt{A_1}+\sqrt{A_2}}{2}\right]^2\)

Question 17. If the central portion of a convex lens is wrapped in black paper as shown in the figure

1. No image will be formed by the remaining portion of the lens
2. The full image will be formed but it will be less bright
3. The central portion of the image will be missing
4. There will be two images each produced by one of the exposed portions of the lens

Answer: 2. The full image will be formed but it will be less bright

Question 18. A convex lens forms a real image of a point object placed on its principal axis. If the upper half of the lens is painted black, the image will

1. Be shifted downwards
2. Be shifted upwards
3. Not be shifted
4. Shift on the principal axis

Answer: 3. Not be shifted

Question 19. In the figure, an air lens of radii of curvature 10 cm (R₁ = R₂ = 10 cm) is cut in a cylinder of glass (p = 1.5). The focal length and the nature of the lens is

1. 15 cm, concave
2. 15 cm, convex
3. ∞, neither concave nor convex
4. 0, concave

Answer: 1. 15 cm, concave

Question 20. A lens made of glass with a refractive index 1.5 has a focal length of 10 cm in air and 50 cm when completely immersed in a liquid. Then the refractive index of the liquid is

1. 1.36
2. 1.33
3. 1.30
4. 1.38

Answer: 1. 1.36

Question 21. The correct conclusion that can be drawn from these figures is

1. μ₁ < μ but μ < μ₂
2. μ₁ > μ but μ < μ₂
3. μ₁ = μ but μ < μ₂
4. μ₁ = μ but μ₂ < μ

Answer: 3. μ₁ = μ but μ < μ₂

Question 22. A magnifying glass is to be used at the fixed object distance of 1 inch. if it is to produce an erect image magnified 5 times, its focal length should be

1. 0.2 inch
2. 0.8 inch
3. 1.25 inch
4. 5 inch

Answer: 3. 1.25 inch

Question 23. A convex lens of focal length f produces a virtual image n times the size of the object. Then the distance of the object from the lens is

1. \(\frac{n-1}{n} f\)
2. \(\frac{n+1}{n} f\)
3. \(\frac{\mathrm{f}}{\mathrm{n}}\)
4. \(\frac{n}{n-1} f\)

Answer: 1. \(\frac{n-1}{n} f\)

Question 24. The focal length of a convex lens made from a material of refractive index 1.52 is 10 cm when placed in air. If it is immersed in carbon disulfide of refractive index 1.68, then its focal length and nature will be

1. + 36.4 cm, convex lens.
2. – 36.4 cm, concave lens.
3. + 54.6 cm, convex lens.
4. – 54.6 cm, concave lens.

Answer: 4. – 54.6 cm, concave lens.

Question 25. Two symmetric double convex lenses A and B have the same focal length, but the radii of curvature differ so that, R_A = 0.9 R_B. If n_A = 1.63, find n_B.

1. 1.7
2. 1.6
3. 1.5
4. 4/3

Answer: 1. 1.7

Question 26. When a lens of power P (in the air) made of material of refractive index μ is immersed in a liquid of refractive index μ₀. Then the power of the lens is:

1. \(\frac{\mu-1}{\mu-\mu_0} \mathrm{P}\)
2. \(\frac{\mu-\mu_0}{\mu-1} \mathrm{P}\)
3. \(\frac{\mu-\mu_0}{\mu-1} \cdot \frac{P}{\mu_0}\)
4. None of these

Answer: 3. \(\frac{\mu-\mu_0}{\mu-1} \cdot \frac{P}{\mu_0}\)

Question 27. A thin symmetrical double convex lens of power P is cut into three parts, as shown in the figure. Power of A is:

1. 2P
2. P/2
3. P/3
4. P

Answer: 4. P

Question 28. A convex lens makes a real image of 4 cm long (height) on a screen. When the lens is shifted to a new position without disturbing the object or the screen, we get a real image on the screen, which is 16 cm long. The length (height) of the object is:

1. 1/4 cm
2. 8 cm
3. 20 cm
4. 2 cm

Answer: 2. 8 cm

Question 29. An object is placed at a distance of 10 cm from a convex lens of power 5D. Find the position of the image:

1. -40 cm
2. 30 cm
3. 20 cm
4. -10 cm

Answer: 3. 20 cm

Question 30. The radius of the convex surface of the plano-convex lens is 20 cm and the refractive index of the material of the lens is 1.5 The focal length is :

1. 30 cm
2. 50 cm
3. 20 cm
4. 40 cm

Answer: 4. 40 cm

Question 31. An asymmetric double convex lens is cut in two equal parts by a plane perpendicular to the principal axis. If the power of the original lens is 4D, the power of a cut lens will be

1. 2D
2. 3D
3. 4D
4. 5D

Answer: 1. 2D

Question 32. A point object is placed at the focus of a double concave lens. The image is formed

1. At infinity
2. Between the focus and the lens
3. At focus
4. Between the focus and infinity

Answer: 2. Between the focus and the lens

Question 33. A thin convex lens with a refractive index of 1.5 is placed in a liquid with a refractive index of 2.0. Then the power of the lens in air is 10 D. Then in the liquid its power will be

1. 20 D
2. 10 D
3. -10 D
4. -5 D

Answer: 4. -5 D

Question 34. A body is located on a wall. Its image of equal size is to be obtained on a parallel wall with the help of a convex lens. The lens is placed at a distance d ahead of the second wall, then the required focal length will be:

1. Only \(\frac{d}{4}\)
2. Only \(\frac{d}{2}\)
3. More than Only \(\frac{d}{4}\) but less than Only \(\frac{d}{2}\)
4. Less than Only \(\frac{d}{4}\)

Answer: 2. Only \(\frac{d}{2}\)

Question 35. An equiconvex lens is cut into two halves along (1) XOX’ and (2) YOY’ as shown in the figure. Let f, f ’,f ’’ be the focal lengths of the complete lens, of each half in case (1), and of each half in case (2), respectively.

Choose the correct statement from the following

1. f ’ = f, f ’’ = f
2. f ’ = 2f, f ’’ = 2f
3. f ’ = f, f ’’ = 2f
4. f ’ = 2f, f ’’ = f

Answer: 3. f ’ = f, f ’’ = 2f

Question 36. A convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens. Then its focal length will:

1. Become small, but non-zero
2. Remain unchanged
3. Become zero
4. Become infinite

Answer: 4. Become infinite

Question 37. A student measures the focal length of a convex lens by putting an object pin at a distance |u| from the lens and measuring the distance ‘v’ of the image pin. The graph between ‘u’ and ‘v’ plotted by the student should look like

Answer: 2

Question 38. The image formed on the retina of the eye is proportional to:

1. Size of object
2. Area of object
3. \(\frac{\text { size of object }}{\text { size of image }}\)
4. \(\frac{\text { size of image }}{\text { size of object }}\)

Answer: 1. Size of object

Question 39. In order to obtain an image on the wall of a bulb at a distance d from the wall a convex lens is placed between the bulb and wall. The focal length of the lens will be

1. d/2
2. Between d/2 and d/4
3. More then d/2
4. Less than d/4

Answer: 4. Less than d/4

Question 40. An object is placed 12 cm to the left of a converging lens of a focal length of 8 cm. Another converging lens of 6 cm focal length is placed at a distance of 30 cm from the object to the right of the first lens. The second lens will produce

1. A virtual enlarged image
2. No image
3. A real inverted image
4. A real enlarged image

Answer: 3. A real inverted image

Question 41. A biconvex lens of focal length f forms a circular image of radius r of the sun in the focal plane. Then which option is correct:

1. πr² ∝ f
2. πr² ∝ f²
3. If a lower half part is covered by a black sheet, then the area of the image is equal to πr²/2
4. If f is doubled, the intensity will increase

Answer: 2. πr² ∝ f²

Question 42. A slide projector magnified a film of 100 cm² on a screen. If linear magnification is 4, then the area of the magnified image will be:

1. 1600 cm²
2. 800 cm²
3. 400 cm²
4. 200 cm²

Answer: 1. 1600 cm²

Chapter 7 Geometrical Optics Combination Of Thin Lens Or Lens And Mirrors

Question 1. A convex lens of focal length 25 cm and a concave lens of focal length 20 cm are mounted coaxially separated by a distance of d cm. If the power of the combination is zero, d is equal to

1. 45
2. 30
3. 15
4. 5

Answer: 4. 5

Question 2. A convex lens of power 4D and a concave lens of power 3D are placed in contact, the equivalent power of combination:

1. 1D
2. D
3. 7D
4. D

Answer: 1. 1D

Question 3. Two thin lenses of power +5D and -2D are placed in contact with each other. The focal length of the combination will behave like a

1. Convex lens of focal length 3m
2. A concave lens of focal length 0.33m
3. Convex lens of focal length 0.33m
4. None of the above

Answer: 3. Convex lens of focal length 0.33m

Question 4. The focal length of a plano-concave lens is -10 cm, then its focal length when its plane surface is polished is (n = 3/2):

1. 20 cm
2. -5 cm
3. 5 cm
4. None of these

Answer: 3. 5 cm

Question 5. A combination of two thin lenses with focal lengths f₁ and f₂ respectively forms an image of a distant object at a distance of 60 cm when lenses are in contact. The position of this image shifts by 30 cm towards the combination when two lenses are separated by 10 cm. The corresponding values of f₁ and f₂ are

1. 30 cm, -60 cm
2. 20 cm, -30cm
3. 15cm, -20 cm
4. 12 cm, -15 cm

Answer: 2. 20 cm, -30cm

Question 6. A plano convex lens (f = 20 cm) is silvered at the plane surface. Now f will be

1. 20 cm
2. 40 cm
3. 30 cm
4. 10 cm

Answer: 4. 10 cm

Question 7. A luminous object is placed at a distance of 30 cm from a convex lens of focal length 20 cm. On the other side of the lens, at what distance from the lens must a convex mirror of radius of curvature 10 cm be placed in order to have an erect image of the object coincident with it?

1. 12 cm
2. 30 cm
3. 50 cm
4. 60cm

Answer: 3. 50 cm

Question 8. The plane surface of a plano-convex lens of focal length f is silvered. It will behave as:

1. Plane mirror
2. Convex mirror of focal length 2f
3. A concave mirror of focal length f/2
4. None of the above

Answer: 3. Concave mirror of focal length f/2

Question 9. A concave lens of focal length 20 cm placed in contact with a plane mirror acts as a:

1. Convex mirror of focal length 10 cm
2. A concave mirror of focal length 40 cm
3. A concave mirror of focal length 60 cm
4. A concave mirror of focal length 10 cm

Answer: 1. Convex mirror of focal length 10 cm

Question 10. A plano-convex lens of focal length 10 cm is silvered at its plane face. The distance d at which an object must be placed in order to get its image on itself is:

1. 5 cm
2. 20 cm
3. 10 cm
4. 2.5 cm

Answer: 3. 10 cm

Question 11. In figure (1) a thin lens of focal length 10 cm is shown. The lens is cut into two equal parts, and the parts are arranged as shown in Figure (2). An object AB of height 1 cm is placed at a distance of 7.5 cm from the arrangement. The height of the final image will be:

1. 0.5 cm
2. 2 cm
3. 1 cm
4. 4 cm

Answer: 2. 2 cm

Question 12. A convex lens of focal length 40 cm is kept in contact with a concave lens of focal length 25 cm. The power of the combination is

1. \(-6.5 \mathrm{D}\)
2. \(+6.5 \mathrm{D}\)
3. \(\frac{f_0}{f_c}-1.5 D\)
4. \(\frac{f_c}{f_o}+1.5 \mathrm{D}\)

Answer: 3. \(\frac{f_0}{f_c}-1.5 D\)

Question 13. The plane faces of two identical plano-convex lenses, each having a focal length of 40 cm, are placed against each other to form a common convex lens. The distance from this lens at which an object must be placed to obtain a real inverted image with magnification equal to unity is

1. 80 cm
2. 40 cm
3. 20 cm
4. 160 cm

Answer: 2. 40 cm

Question 14. A convex lens and a concave lens, each having the same focal length of 25 cm, are put in contact to form a combination of lenses. The power in diopters of the combination is:

1. 25
2. 50
3. Infinite
4. Zero

Answer: 4. Zero

Question 15. A plano-convex lens with a refractive index of 1.5 and a radius of curvature of 30 cm is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of the size of the object?

1. 20 cm
2. 30 cm
3. 60 cm
4. 80 cm

Answer: 1. 20 cm

Question 16. A plano-convex lens is made of a material with a refractive index p = 1.5. The radius of curvature of the curved surface of the lens is 20 cm. If its plane surface is silvered, the focal length of the silvered lens will be:

1. 10 cm
2. 20 cm
3. 40 cm
4. 80 cm

Answer: 2. 20 cm

Question 17. power of the combination of two lenses of focal lengths 20 cm and 25 cm respectively:

1. + 1 D
2. + 9 D
3. – 1 D
4. – 9 D

Answer: 2. + 9 D

Chapter 7 Geometrical Optics Dispersion Of Light

Question 1. Dispersive power of a prism depends on-

1. Material
2. Prism angle
3. Shape of prism
4. Angle on incidence

Answer: 1. Material

Question 2. When light is passed through a prism, the color which deviates least is:

1. Red
2. violet
3. Blue
4. Green

Answer: 1. Red

Question 3. If the refractive index of red, violet, and yellow lights are 1.42, 1.62, and 1.50 respectively for a medium, its dispersive power will be

1. 0.4
2. 0.3
3. 0.2
4. 0.1

Answer: 1. 0.4

Question 4. Two thin lenses, one convex of focal length 30 cm and the other concave of focal length 10cm are put into contact. If this combination is equivalent to an achromatic lens then the ratio of dispersive powers (ω₁,/ω₂) of the above two lenses is

1. 1/3
2. – 3
3. 3
4. – 1/3

Answer: 3. 3

Question 5. The colors are characterized by which of the following characteristics of light-

1. Frequency
2. Amplitude
3. Wavelength
4. Velocity

Answer: 1. Frequency

Question 6. The dispersion of light in a medium implies that :

1. Lights of different wavelengths travel at different speeds in the medium
2. Lights of different frequencies travel at different speeds in the medium
3. The refractive index of a medium is different for different wavelengths
4. All of the above.

Answer: 4. All of the above.

Question 7. The critical angle of light passing from glass to air is minimal for

1. Red
2. Green
3. Yellow
4. Violet

Answer: 4. Violet

Question 8. A plane glass slab is placed over various colored letters. The letter which appears to be raised the least is:

1. Violet
2. Yellow
3. Red
4. Green

Answer: 3. Red

Question 9. A medium has n_v = 1.56, n_r = 1.44. Then its dispersive power is:

1. 3/50
2. 6/25
3. 0.03
4. None of these

Answer: 2. 6/25

Question 10. All the listed things below are made of flint glass. Which one of these has the greatest dispersive power (ω)?

1. Prism
2. Glass slab
3. Biconvex lens
4. All have same

Answer: 4. All have the same

Question 11. Light of wavelength 4000 Å is incident at a small angle on a prism of apex angle 4°. The prism has n_v = 1.5 and n_r = 1.48. The angle of dispersion produced by the prism in this light is:

1. 0.2°
2. 0.08°
3. 0.192°
4. None of these

Answer: 4. None of these

Question 12. When white light passes through a glass prism, one gets a spectrum on the other side of the prism. In the emergent beam, the ray which is deviating least is or Deviation by a prism is lowest for

1. Violet ray
2. Green ray
3. Red ray
4. Yellow ray

Answer: 3. Red ray

Question 13. A spectrum is formed by a prism of dispersive power ω. If the angle of deviation is ‘δ’, then the angular dispersion is

1. ω/δ
2. δ/ω
3. 1/ ωδ
4. ωδ

Answer: 4. ωδ

Question 14. When white light passes through the achromatic combination of prisms, then what is observed

1. Only deviation
2. Only dispersion
3. Deviation and dispersion
4. None of the above

Answer: 1. Only deviation

Question 15. An achromatic combination of lenses is formed by joining

1. 2 convex lenses
2. 2 concave lenses
3. 1 convex lens and 1 concave lens
4. Convex lens and plane mirror

Answer: 3. 1 convex lens and 1 concave lens

Question 16. An achromatic convergent doublet of two lenses in contact has a power of + 2D. The convex lens has power + 5 D. What is the ratio of the dispersive powers of the convergent and divergent lenses?

1. 2: 5
2. 3: 5
3. 5: 2
4. 5: 3

Answer: 2. 3: 5

Question 17. The ratio of the angle of minimum deviation of a prism when dipped in water and when in the air will be (_aμ_g = 3/2 and _aμ_w = 4/3) If the prism angle is very small

1. 1/8
2. 1/2
3. 3/4
4. 1/4

Answer: 4. 1/4

Question 18. The respective angles of the flint and crown glass prisms are A’ and A. They are to be used for dispersion without deviation, then the ratio of their angles A’/A will be

1. \(-\frac{\left(\mu_y-1\right)}{\left(\mu_y{ }^{\prime}-1\right)}\)
2. \(-\frac{\left(\mu_y{ }^{\prime}-1\right)}{\left(\mu_y-1\right)}\)
3. \(\left(\mu_y{ }^{\prime}-1\right)\)
4. \(\left(\mu_y-1\right)\)

Answer: 1. \(-\frac{\left(\mu_y-1\right)}{\left(\mu_y{ }^{\prime}-1\right)}\)

Question 19. The focal length of a convex lens will be the maximum for

1. Blue light
2. Yellow light
3. Greenlight
4. Red light

Answer: 4. Red light

Question 20. Rainbows are formed by:

1. Reflection and diffraction
2. Refraction and scattering
3. Dispersion and total internal reflection
4. Interference only

Answer: 3. Dispersion and total internal reflection

Question 21. The ratio of the refractive index of red light to blue light in air is

1. Less than unity
2. Equal to unity
3. Greater than unity
4. Less as well as greater than unity depending upon the experimental arrangement

Answer: 1. Less than unity

Question 22. The refractive index of a piece of transparent quartz is the greatest for

1. Red light
2. Violet light
3. Greenlight
4. Yellow light

Answer: 2. Violet light

Question 23. The refractive index for a material for infrared light is

1. Equal to that of ultraviolet light
2. Less than that for ultraviolet light
3. Equal to that for the red color of light
4. Greater than that for ultraviolet light

Answer: 2. Less than that for ultraviolet light

Question 24. With respect to air critical angle in a medium for the light of red color λ₁ is θ. Other facts remain the same, the critical angle for the light of yellow color [λ₂] will be

1. θ
2. More than θ
3. Less than θ
4. None of these

Answer: 3. Less than θ

Question 25. A beam of light composed of red and green rays is incident obliquely at a point on the face of a rectangular glass slab. When coming out of the opposite parallel face, the red and green rays emerge from:

1. Two points propagating in two different non-parallel directions
2. Two points propagating in two different parallel directions
3. One point propagating in two different directions
4. One point propagating in the same direction

Answer: 2. Two points propagating in two different parallel directions

Chapter 7 Geometrical Optics Defects Of Vision

Question 1. A shortsighted person can read a book clearly at a distance of 10 cm from the eyes. The lenses required to read the book kept at 60cm are :

1. Convex lenses of focal length 30 cm
2. Convex lenses of focal length 30 cm
3. Convex lenses of focal length 12 cm
4. Concave lenses of focal length 12 cm

Answer: 4. Concave lenses of focal length 12 cm

Question 2. A person can’t see the objects clearly placed at a distance of more than 40 cm. He is advised to use a lens of power –

1. + 2.5 D
2. – 2.5 D
3. + 0.4 D
4. – 0.4 D

Answer: 2. – 2.5 D

Question 3. A person can see clearly only up to a distance of 25cm. He wants to read a book placed at a distance of 50cm. What kind of lens does he require for his spectacles and what must be its power?

1. Concave, – 1.0 D
2. Convex, + 1.5 D
3. Concave, – 2.0 D
4. Convex, + 2.0 D

Answer: 4. Convex, + 2.0 D

Question 4. Astigmatism (for the human eye) can be removed by using

1. Concave lens
2. Convex lens
3. Cylindrical lens
4. Prismatic lens

Answer: 3. Cylindrical lens

Question 5. The circular part in the center of the retina is called

1. Blind spot
2. Yellow spot
3. Red spot
4. None of the above

Answer: 2. Yellow spot

Question 6. A person cannot see distinctly at a distance of less than one meter. Calculate the power of the lens that he should use to read a book at a distance of 25 cm

1. +3.0 D
2. +0.125D
3. -3.0 D
4. +4.0 D

Answer: 1. +3.0 D

Question 7. A person who can see things most clearly at a distance of 10 cm, requires spectacles to enable them to see clearly things at a distance of 30 cm. What should be the focal length of the spectacles?

1. 15 cm (concave)
2. 15 cm (convex)
3. 10 cm
4. 0

Answer: 1. 15 cm (concave)

Question 8. The power of a lens used by a short-sighted person is – 2 D. Find the maximum distance of an object, which he can see without spectacles

1. 25 cm
2. 50 cm
3. 100 cm
4. 10 cm

Answer: 2. 50 cm

Chapter 7 Geometrical Optics Optical Instrument

Question 1. A simple microscope has a focal length of 5 cm. The magnification at the least distance of distinct vision is-

1. 1
2. 5
3. 4
4. 6

Answer: 4. 6

Question 2. In a compound microscope, the intermediate image is –

1. Virtual, erect, and magnified
2. Real, erect, and magnified
3. Real, inverted, and magnified
4. Virtual, erect, and reduced

Answer: 3. Real, inverted, and magnified

Question 3. The resolving power of a telescope is more when its objective lens has

1. Greater focal length
2. Smaller focal length
3. Greater diameter
4. Smaller diameter

Answer: 3. Smaller focal length

Question 4. A Galileo telescope has an objective of focal length 100 cm & magnifying power of 50. The distance between the two lenses in normal adjustment will be

1. 150 cm
2. 100 cm
3. 98 cm
4. 200 cm

Answer: 3. 98 cm

Question 5. The convex lens is used in

1. Microscope
2. Telescope
3. Projector
4. All of the above

Answer: 4. All of the above

Question 6. The magnifying power of a simple microscope can be increased if an eyepiece of:

1. A shorter focal length is used
2. A longer focal length is used
3. A shorter diameter is used
4. A longer diameter is used

Answer: 1. Shorter focal length is used

Question 7. The focal length of the objective of a microscope is

1. Arbitrary
2. Less than the focal length of the eyepiece
3. Equal to the focal length of the eyepiece
4. Greater than the focal length of the eyepiece

Answer: 2. Less than the focal length of the eyepiece

Question 8. The resolving power of a microscope depends upon

1. The focal length and aperture of the eye lens
2. The focal lengths of the objective and the eye lens
3. The apertures of the objective and the eye lens
4. The wavelength of light illuminating the object

Answer: 4. The wavelength of light illuminating the object

Question 9. An astronomical telescope has an eyepiece of focal length 5 cm. If the angular magnification in normal adjustment is 10, when the final image is at least a distance of distinct vision (25cm) from the eyepiece, then angular magnification will be:

1. 10
2. 12
3. 50
4. 60

Answer: 2. 12

Question 10. A person with a defective sight is using a lens having a power of +2D. The lens he is using is

1. A concave lens with f = 0.5 m
2. A convex lens with f = 2.0 m
3. A concave lens with f = 0.2 m
4. A convex lens with f = 0.5 m

Answer: 4. Convex lens with f = 0.5 m

Question 11. The focal lengths of the objective and eye lens of a microscope are 1 cm and 5 cm respectively. If the magnifying power for the relaxed eye is 45, then the length of the tube is

1. 30 cm
2. 25 cm
3. 15 cm
4. 12 cm

Answer: 3. 15 cm

Question 12. In a compound microscope magnification will be large, if the focal length of the eyepiece is:

1. Large
2. Smaller
3. Equal to that of objective
4. Less than that of objective

Answer: 2. Smaller

Question 13. The focal length of the objective lens of a compound microscope is :

1. Equal to the focal length of its eyepiece
2. Less than the focal length of the eyepiece
3. Greater than the focal length of the eyepiece
4. Any of the above three

Answer: 2. Less than the focal length of the eyepiece

Question 14. Microscope is an optical instrument which :

1. Enlarges the object
2. Increases the visual angle formed by the object at the eye
3. Decreases the visual angle formed by the object at the eye
4. Brings the object nearer

Answer: 2. Increases the visual angle formed by the object at the eye

Question 15. For which of the following colors, the magnifying power of a microscope will be maximum:

1. White colour
2. Red colour
3. Violet colour
4. Yellow colour

Answer: 3. Violet colour

Question 16. The length of the compound microscope is 14 cm. The magnifying power for the relaxed eye is 25. If the focal length of the eye lens is 5 cm, then the object distance for the objective lens will be:

1. 1.8 cm
2. 1.5 cm
3. 2.1 cm
4. 2.4 cm

Answer: 1. 1.8 cm

Question 17. If the focal length of the objective and eye lens are 1.2 cm and 3 cm respectively and the object is put 1.25cm away from the objective lens the final image is formed at infinity. The magnifying power of the microscope is:

1. 150
2. 200
3. 250
4. 400

Answer: 2. 200

Question 18. When the object is self-luminous, the resolving power of a microscope is given by the expression:

1. \(\frac{2 \mu \sin \theta}{1.22 \lambda}\)
2. \(\frac{\mu \sin \theta}{\lambda}\)
3. \(\frac{2 \mu \cos \theta}{1.22 \lambda}\)
4. \(\frac{2 \mu}{\lambda}\)

Answer: 1. \(\frac{2 \mu \sin \theta}{1.22 \lambda}\)

Question 19. the focal length of the objective and eye lens of an astronomical telescope are respectively 2m and 5 cm. The final image is formed at (1) the least distance of distinct vision and (2) infinity. The magnifying power in both cases will be:

1. –48, –40
2. –40, –48
3. –40, 48
4. –48, 40

Answer: 1. –48, –40

Question 20. For observing a cricket match, a binocular is preferred to a terrestrial telescope because:

1. The binocular gives the proper three-dimensional view
2. The binocular has a shorter length
3. The telescope does not give an erect image
4. Telescopes have chromatic aberrations

Answer: 1. The binocular gives the proper three-dimensional view

Question 21. An astronomical telescope has an angular magnification of magnitude 5 for distant objects. The separation between the objective and the eyepiece is 36 cm and the final image is formed at infinity. The focal length f₀ of the objective and the focal length f_e of the eyepiece are:

1. f₀ = 45 cm and f_e = –9 cm
2. f₀ = 7.2 cm and f_e = 5 cm
3. f₀ = 50 cm and f_e = 10 cm
4. f₀ = 30 cm and f_e = 6 cm

Answer: 4. f₀ = 30 cm and f_e = 6 cm

Question 22. In the Galilean telescope, if the powers of an objective and eye lens are respectively +1.25 D and -20D, then for relaxed vision, the length and magnification will be:

1. 21.25 cm and 16
2. 75 cm and 20
3. 75 cm and 16
4. 8.5 cm and 21.25

Answer: 3. 75 cm and 16

Question 23. An astronomical telescope has two lenses of focal powers 0.5 D and 20D. Then its magnifying power will be:

1. 8
2. 20
3. 30
4. 40

Answer: 4. 40

Question 24. The magnifying power of the objective of a compound microscope is 7. If the magnifying power of a microscope is 35, the magnifying power of the eye lens will be:

1. 5
2. 30
3. 35
4. 28

Answer: 1. 5

Question 25. For a telescope, larger the diameter of the objective lens

1. Greater is the resolving power
2. Smaller is the resolving power
3. Greater is the magnifying power
4. Smaller is the magnifying power

Answer: 1. Greater is the resolving power

Question 26. The focal length of the objective and eye-piece of a telescope are respectively 100 cm and 2 cm. The moon subtends an angle of 0.5° at the eye. If it is looked through the telescope, the angle subtended by the moon’s image will be

1. 100°
2. 50°
3. 25°
4. 10°

Answer: 3. 25°

Question 27. The focal lengths of the objective and eyepiece of a microscope are 4 cm and 8 cm respectively and the distance of the object from the objective lens is 4.5 cm then magnifying power is:

1. 18
2. 32
3. 64
4. 20

Answer: 2. 32

Question 28. When the length of the tube of the microscope is increased then the magnifying power :

1. Decreases
2. Increases
3. Remains unchanged
4. May decrease or increase

Answer: 1. Decreases

Question 29. An electron microscope is better than an optical microscope, because of :

1. More resolving power
2. Comfortable use
3. Low purchasing cost
4. Observation can be taken fastly

Answer: 1. More resolving power

Question 30. For a compound microscope, the focal lengths of the object lens and eye lens are f₀ and f_e respectively, then magnification will be done by a microscope when

1. f₀ = f_e
2. f₀ > f_e
3. f₀ < f_e
4. None of these

Answer: 3. f₀ < f_e

Question 31. An astronomical telescope has a large aperture to

1. Reduce spherical aberration
2. Have high resolution
3. Increase the span of observation
4. Have low dispersion

Answer: 2. Have high resolution

Question 32. The wavelength of light used in an optical instrument is λ₁ = 4000 Å and λ₂ = 5000 Å, then the ratio of their respective resolving powers (corresponding to λ₁ and λ₂) is

1. 16: 25
2. 9: 1
3. 4: 5
4. 5: 4

Answer: 4. 5: 4

Question 33. The image formed by an objective of a compound microscope is

1. Virtual and diminished
2. Real and diminished
3. Real and enlarged
4. Virtual and enlarged

Answer: 3. Real and enlarged

Chapter 7 Geometrical Optics Exercise 2 Multiple Choice Questions And Answers

Question 1. A person’s eye is at a height of 1.5 m. He stands in front of a 0.3m long plane mirror which is 0.8 m above the ground. The length of the image he sees of himself is:

1. 1.5m
2. 1.0m
3. 0.8m
4. 0.6m

Answer: 4. 0.6m

Question 2. A point object is kept in front of a plane mirror. The plane mirror is performing SHM of amplitude 2 cm. The plane mirror moves along the x-axis and the x-axis is normal to the mirror. The amplitude of the mirror is such that the object is always in front of the mirror. The amplitude of the SHM of the image is

1. Zero
2. 2 cm
3. 4 cm
4. 1 cm

Answer: 3. 4 cm

Question 3. In the figure shown, the image of a real object is formed at the point I. AB is the principal axis of the mirror. The mirror must be:

1. Concave and placed towards the right of the I
2. Concave and placed towards the left of the I
3. Convex and placed towards the right of the I
4. Convex and placed towards the left of I

Answer: 2. Concave and placed towards the left of I

Question 4. AB is an incident beam of light and DC is a reflected beam (the number of reflections for this may be 1 or more than 1) of light. AB and DC are separated by some distance (maybe large). It is possible by placing what type of mirror on the right side.

1. Two plane mirror
2. One concave mirror
3. One prism
4. All of the above

Answer: 4. All of the above

Question 5. A point object at 15 cm from a concave mirror of a radius of curvature of 20 cm is made to oscillate along the principal axis with an amplitude of 2 mm. The amplitude of its image will be

1. 2 mm
2. 4 mm
3. 8 mm
4. 16 mm

Answer: 3. 8 mm

Question 6. The distance between an object and its doubly magnified image by a concave mirror is: [Assume f = focal length]

1. 3 f/2
2. 2 f/3
3. 3 f
4. Depends on whether the image is real or virtual.

Answer: 1. 3 f/2

Question 7. A ray of light is incident on a parallel slab of thickness t and refractive index n. If the angle of incidence θ is small, then the displacement in the incident and emergent ray will be:

1. \(\frac{t \theta(n-1)}{n}\)
2. \(\frac{t \theta}{n}\)
3. \(\frac{t \theta n}{n-1}\)
4. None

Answer: 1. \(\frac{t \theta(n-1)}{n}\)

Question 8. A concave spherical surface with a radius of curvature 10 cm separates two mediums X and Y of refractive indices 4/3 and 3/2 respectively. The Centre of curvature of the surface lies in the medium X. An object is placed in medium X.

1. Image is always real
2. The image is real if the object’s distance is greater than 90 cm.
3. Image is always virtual
4. The image is virtual only if the object’s distance is less than 90 cm.

Answer: 3. Image is always virtual

Question 9. The observer ‘O’ sees the distance AB as infinitely large. If the refractive index of the liquid is μ₁ and that of glass is μ₂, then \(\frac{\mu_1}{\mu_2}\) is:

1. 2
2. 1/2
3. 4
4. None of these

Answer: 1. 2

Question 10. In the given figure a plano-concave lens is placed on a paper on which a flower is drawn. How far above its actual position does the flower appear to be?

1. 10 cm
2. 15 cm
3. 50 cm
4. None of these

Answer: 1. 10 cm

Question 11. The focal lengths of the objective & the eyepiece of a compound microscope are 1 cm and 5 cm respectively. An object placed at a distance of 1.1 cm from the objective has its final image formed at 25 cm from the eyepiece. The length of the microscope tube is:

1. 6.1 cm
2. 49/8 cm
3. 6 cm
4. 91/6 cm

Answer: 4. 91/6 cm

Question 12. A concave mirror of focal length 15 cm forms an image having twice the linear dimension (height) of the object. The position of the object when the image is virtual will be:

1. 45 cm
2. 30 cm
3. 7.5 cm
4. 22.5 cm

Answer: 3. 7.5 cm

Question 13. Four lenses are made from the same type of glass. The radius of curvature of each face is given below. Which will have the greatest positive power?

1. 10 cm convex and 15 concave
2. 5 cm convex and 10 cm concave
3. 15 cm convex and plane
4. 20 cm convex and 30 cm concave

Answer: 2. 5 cm convex and 10 cm concave

Question 14. A prism of refractive index has a refracting angle of 60°. Ar what angle a ray must be incident on it so that it suffers a minimum deviation?

1. 45°
2. 60°
3. 90°
4. 180°

Answer: 1. 45°

Question 15. The refractive index of the material of the prism and liquid are 1.56 and 1.32 respectively. What will be the value of θ for the following refraction?

1. \(\sin \theta>\frac{13}{11}\)
2. \(\sin \theta>\frac{11}{13}\)
3. \(\sin \theta>\frac{\sqrt{3}}{2}\)
4. \(\sin \theta>\frac{1}{\sqrt{2}}\)

Answer: 2. \(\sin \theta>\frac{11}{13}\)

Question 16. In a laboratory four convex lenses L₁, L₂, L₃, and L₄ of focal lengths 2, 4, 6, and 8 cm, respectively are available. Two of these lenses form a telescope of length 10 cm and magnifying power 4. The objective and eye lenses are respectively

1. L₂, L₃,
2. L₂, L₄
3. L₁, L₂,
4. L₄, L₁

Answer: 4. L₄, L₁

Question 17. Distance stars are viewed with the help of an astronomical telescope. The angular separation between two stars can be just resolved by the telescope.

1. Is independent of the diameter of the aperture of the telescope
2. Increases with the increases in the diameter of the aperture of the telescope
3. Decreases with the increase in the diameter of the telescope aperture
4. Increases quadratically with the diameter of the telescope aperture

Answer: 3. Decreases with the increase in the diameter of the telescope aperture

Question 18. The refractive index of water is 5/3. A light source is placed in water at a depth of 4 m. Then what must be the minimum radius of the disc placed on the water surface so that the light of the source can be stopped?

1. 3 m
2. 4 m
3. 5 m
4. ∞

Answer: 1. 3 m

Question 19. Statement-1: The formula connecting u, v, and f for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.

Statement-2: Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

1. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
2. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
3. Statement-1 is True, Statement-2 is False
4. Statement-1 is False, and Statement-2 is True.

Answer: 3. Statement-1 is True, Statement-2 is False

Chapter 7 Geometrical Optics Exercise 3 Multiple Choice Questions And Answers

Question 1. A boy is trying to start a fire by focusing sunlight on a piece of paper using a biconvex lens with a focal length of 10 cm. The diameter of the sun is 1.39 x 10⁹ m and its mean distance from the earth is 1.5 x 10¹¹ m. What is the diameter of the sun’s image on the paper?

1. 9.2 x 10^-4 m
2. 6.5 x 10^-4 m
3. 6.5 x 10^-5 m
4. 12.4 x 10^-4 m

Answer: 1. 9.2 x 10^-4 m

Question 2. Two thin lenses of focal lengths f₁ and f₂ are in contact and coaxial. The power of the combination is:

1. \(\sqrt{\frac{f_1}{f_2}}\)
2. \(\sqrt{\frac{f_2}{f_1}}\)
3. \(\frac{f_1-f_2}{f_2 f_1}\)
4. \(\frac{f_1+f_2}{f_1 f_2}\)

Answer: 4. \(\frac{f_1+f_2}{f_1 f_2}\)

Question 3. A ray of light traveling in a transparent medium of refractive index μ falls on a surface separating the medium from the air at an angle of incidence of 45°. For which of the following values of μ the ray can undergo total internal reflection?

1. μ = 1.33
2. μ = 1.40
3. μ = 1.50
4. μ = 1.25

Answer: 3. μ = 1.50

Question 4. A lens having focal length f and aperture of diameter d forms an image of intensity I. The aperture of diameter in the central region of the lens is covered by black paper. The focal length of the lens and intensity of the image now will be respectively

1. f and \(\frac{I}{4}\)
2. \(\frac{3 \mathrm{f}}{4}\) and \(\frac{I}{2}\)
3. f and \(\frac{3 I}{4}\)
4. \(\frac{\mathrm{f}}{2}\) and \(\frac{\mathrm{I}}{2}\)

Answer: 3. f and \(\frac{3 I}{4}\)

Question 5. The speed of light in media M₁ and M₂ are 1.5 × 10⁸ m/s and 2.0 × 10⁸ m/s respectively. A ray of light enters from medium M₂ to M₂ at an incidence angle i. If the ray suffers total internal reflection, the value of i is

1. Equal to \(\sin ^{-1}\left(\frac{2}{3}\right)\)
2. Equal to or less than \(\sin ^{-1}\left(\frac{3}{5}\right)\)
3. Equal to or greater than \(\sin ^{-1}\left(\frac{3}{4}\right)\)
4. Less than \(\sin ^{-1}\left(\frac{2}{3}\right)\)

Answer: 3. Equal to or greater than \(\sin ^{-1}\left(\frac{3}{4}\right)\)

Question 6. A ray of light is incident on a 60° prism at the minimum deviation position. The angle of refraction at the first face (i.e., incident face) of the prism is

1. Zero
2. 30°
3. 45°
4. 60°

Answer: 2. 30°

Question 7. Which of these is not due to total internal reflection?

1. Working with optical fiber
2. Difference between the apparent and real depth of the pond
3. Mirage on hot summer days
4. Brilliance of diamond

Answer: 2. Difference between apparent and real depth of the pond

Question 8. The dimensions of (μ₀∈₀)-½are:

1. [L^1/2 T^-1/2]
2. [L^-1 T]
3. [L T^-1]
4. [L^-1/2 T^1/2]

Answer: 3. [L T^-1]

Question 9. A biconvex lens has a radius of curvature of magnitude 20 cm. Which one of the following options describes best the image formed of an object of height 2 cm placed 30 cm from the lens? (Refractive index of lens material = 1.5)

1. Virtual, upright, height = 1 cm
2. Virtual, upright, height = 0.5 cm
3. Real, inverted, height = 4 cm
4. Real, inverted, height = 1cm

Answer: 3. Real, inverted, height = 4 cm

Question 10. A thin prism of angle 15º made of glass of refractive index µ₁ = 1.5 is combined with another prism of glass of refractive index µ₂ = 1.75. The combination of the prism produces dispersion without deviation. The angle of the second prism should be:

1. 7º
2. 10º
3. 12º
4. 5º

Answer: 2. 10º

Question 11. A conversing beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is:

1. –10 cm
2. 20 cm
3. –30 cm
4. 5 cm

Answer: 3. –30 cm

Question 12. When a biconvex lens of glass having a refractive index of 1.47 is dipped in a liquid, it acts as a plane sheet of glass. This implies that the liquid must have a refractive index.

1. Equal to that of glass
2. Less then one
3. Greater than that of glass
4. Less than that of glass

Answer: 1. Equal to that of glass

Question 13. A ray of light is incident at an angle of incidence, i, on one face of the prism of angle A (assumed to be small), and emerges normally from the opposite face. If the refractive index of the prism is μ, the angle of incidence i, is nearly equal to:

1. μA
2. A/μ
3. A/2μ

Answer: 1. μA

Question 14. A concave mirror of focal length ‘f₁’ is placed at a distance of ‘d’ from a convex lens of focal length ‘f₂’ A beam of light coming from infinity and falling on this convex lens – concave mirror combination returns to infinity. The distance ‘d’ must equal:

1. f₁ + f₂
2. –f₁ + f₂
3. 2f₁ + f₂
4. –2f₁ + f₂

Answer: 3. 2f₁ + f₂

Question 15. The magnifying power of a telescope is 9. When it is adjusted for parallel rays the distance between the objective and eyepiece is 20 cm. The focal lengths of lenses are:

1. 10 cm, 10 cm
2. 15 cm, 5 cm
3. 18 cm, 2 cm
4. 11 cm, 9 cm

Answer: 3. 18 cm, 2 cm

Question 16. The dimensions of (μ₀ε₀)^-1/2 are:

1. [L^1/2T^-1/2]
2. [L^-1T]
3. [LT^-1]
4. [L^1/2T^1/2]

Answer: 3. [LT^-1]

Question 17. A plano convex lens fits exactly into a plano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices μ₁ and μ₂ and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is:

1. \(\frac{\mathrm{R}}{2\left(\mu_1-\mu_2\right)}\)
2. \(\frac{R}{\left(\mu_1-\mu_2\right)}\)
3. \(\frac{2 R}{\left(\mu_2-\mu_1\right)}\)
4. \(\frac{\text { [NEET }}{2\left(\mu_1+\mu_2\right)}\)

Answer: 2. \(\frac{R}{\left(\mu_1-\mu_2\right)}\)

Question 18. For a normal eye, the cornea of the eye provides a converging power of 40 D, and the least converging power of the eye lens behind the cornea is 20 D. Using this information, the distance between the retina and the cornea-eye lens can be estimated to be:

1. 2.5 cm
2. 1.67 cm
3. 1.5 cm
4. 5 cm

Answer: 2. 1.67 cm

Question 19. If the focal length of the objective lens is increased then the magnifying power of:

1. The microscope will increase but that of the telescope decrease
2. Microscope and telescope both will increase
3. Microscope and telescope both will decrease
4. Microscope will decrease but that of telescope will increase.

Answer: 4. Microscope will decrease but that of telescope will increase.

Question 20. The refracting angle of a prism ‘A’, and the refractive index of the material of the prism is cot(A/2). The angle of minimum deviation is:

1. 180° – 2A
2. 90° – A
3. 180° + 2A
4. 180° – 3A

Answer: 1. 180° – 2A

Question 21. Two identical thin plano-convex glass lenses (refractive index × 1.5) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the center. The intervening space is filled with oil with a refractive index of 1.7. The focal length of the combination is:

1. –25 cm
2. –50 cm
3. 50 cm
4. –20 cm

Answer: 2. –50 cm

Question 22. A beam of light consisting of red, green, and blue colors is incident on a right-angled prism. The refractive index of the material of the prism for the above red, green, and blue wavelengths are 1.39, 1.44, and 1.47, respectively.

The prism will:

1. Separate all three colors from one another
2. Not separate the three colors at all
3. Separate the red color part from the green and blue colors
4. Separate the blue colored part from the red and green colors

Answer: 3. Separate the red color part from the green and blue colors

Question 23. In an astronomical telescope in normal adjustment, a straight black line of length L is drawn on the inside part of the objective lens. The eye-piece forms a real image of this line. The length of this image is I. The magnification of the telescope is:

1. \(\frac{\mathrm{L}}{\mathrm{I}}-1\)
2. \(\frac{\mathrm{L}+\mathrm{I}}{\mathrm{L}-\mathrm{I}}\)
3. \(\frac{\mathrm{L}}{\mathrm{I}}\)
4. \(\frac{\mathrm{L}}{\mathrm{I}}+1\)

Answer: 3. \(\frac{\mathrm{L}}{\mathrm{I}}\)

Question 24. Match the corresponding entries of column–1 with column–2. [Where m is the magnification produced by the mirror]

1. A → c and d; B → b and d; C → b and c; D → a and d
2. A → b and c; B → b and c; C → b and d; D → a and d
3. A → a and c; B → a and d; C → a and b; D → c and d
4. A → a and d; B → b and c; C → b and d; D → b and c

Answer: 2. A → b and c; B → b and c; C → b and d; D → a and d

Question 25. An astronomical telescope has an objective and eyepiece of focal lengths of 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance:

1. 54.0 cm
2. 37.3 cm
3. 46.0 cm
4. 50.0 cm

Answer: 1. 54.0 cm

Question 26. The angle incidence for a ray of light at a refracting surface of a prism is 45°. The angle of the prism is 60°. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are

1. \(30^{\circ} ; \frac{1}{\sqrt{2}}\)
2. \(45^{\circ} ; \frac{1}{\sqrt{2}}\)
3. \(30^{\circ} ; \sqrt{2}\)
4. \(45^{\circ} ; \sqrt{2}\)

Answer: 3. \(30^{\circ} ; \sqrt{2}\)

Question 27. A person can see clearly only when they lie between 50 cm and 400 cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use, will be:

1. Conveys, +0.15 diopter
2. Conveys, +2.25 diopter
3. Conveys, -0.25 diopter
4. Conveys, -0.2 diopter

Answer: 3. Conves, -0.25 diopter

Question 28. Two identical glass (μ_g = 3/2) biconvex lenses of focal length f each are kept in contact. The space between those two lenses is filled with water (μ_w = 4/3). The focal length of the combination is

1. \(\frac{3 f}{4}\)
2. \(\frac{f}{3}\)
3. \(\mathrm{f}\)
4. \(\frac{4 f}{3}\)

Answer: 1. \(\frac{3 f}{4}\)

Question 29. An air bubble in a glass slab with a refractive index of 1.5 (near normal incidence) is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness (in cm) of the slab is

1. 16
2. 8
3. 10
4. 12

Answer: 4. 12

Question 30. A thin prism having a refracting angle of 10° is made of glass with a refractive index of 1.42. This prism is combined with another thin prism of glass with a refractive index of 1.7. This combination produces dispersion without deviation. The refracting angle of the second prism should be:

1. 4°
2. 6°
3. 8°
4. 10°

Answer: 2. 6°

Question 31. A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle θ, the spot of the light is found to move through a distance y on the scale. The angle θ is given by:

1. \(\frac{y}{2 x}\)
2. \(\frac{y}{x}\)
3. \(\frac{x}{2 y}\)
4. \(\frac{x}{y}\)

Answer: 1. \(\frac{y}{2 x}\)

Question 32. An astronomical refracting telescope will have large angular magnification and high angular resolution when it has an objective lens of

1. Small focal length and large diameter
2. Small focal length and small diameter
3. Large focal length and large diameter
4. Large focal length and small diameter

Answer: 3. Large focal length and large diameter

Question 33. The refractive index of the material of a prism is √2 and the angle of the prism is 30°. One of the two refracting surfaces of the prism is made a mirror inwards, by a silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is

1. 60°
2. zero
3. 30°
4. 45°

Answer: 4. 45°

Question 34. An object is placed at a distance of 40 cm from a concave mirror of a focal length of 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be

1. 30 cm away from the mirror
2. 36 cm towards the mirror
3. 30 cm towards the mirror
4. 36 cm away from the mirror

Answer: 4. 36 cm away from the mirror

Question 35. Pick the wrong answer in the context of the rainbow.

1. Rainbow is a combined effect of dispersion, refraction, and reflection of sunlight.
2. When the light rays undergo two internal reflections in a water drop, a secondary rainbow is formed.
3. The order of colors is reversed in the secondary rainbow.
4. An observer can see a rainbow when his front is towards the sun.

Answer: 4. An observer can see a rainbow when his front is towards the sun.

Question 36. In total internal reflection when the angle of incidence is equal to the critical angle for the pair of the medium in contact, what will be the angle of refraction?

1. 90°
2. 180°
3. 0°
4. Equal to the angle of incidence

Answer: 1. 90°

Question 37. Two similar thin equi-convex lenses, of focal f each, are kept coaxially in contact with each other such that the focal length of the combination is F₁ When the space between the two lenses is filled with glycerin (which has the same refractive index (μ = 1.5) as that of glass) then the equivalent focal length is F₂. The ratio F₁ : F₂ will be

1. 3: 4
2. 2: 1
3. 1: 2
4. 2 : 3

Answer: 3. 1: 2

Question 38. An equiconvex lens has power P. It is cut into two symmetrical halves by a plane containing the principal axis. The power of one part will be,

1. 0
2. P/2
3. P/4
4. P

Answer: 4. P

Question 39. A double convex lens has a focal length of 25 cm. The radius of curvature of one of the surfaces is double that of the other. Find the radii if the refractive index of the material of the lens is 1.5.

1. 100 cm, 50 cm
2. 25 cm, 50 cm
3. 18.75 cm, 37.5 cm
4. 50 cm, 100 cm

Answer: 3. 18.75 cm, 37.5 cm

Question 40. A plano-convex lens of unknown material and unknown focal length is given. With the help of a spherometer, we can measure the

1. The focal length of the lens
2. The radius of curvature of the curved surface
3. The aperture of the lens
4. The refractive index of the material

Answer: 2. Radius of curvature of the curved surface

Question 41. An object is placed on the principal axis of a concave mirror at a distance of 1.5 f (f is the focal length). The image will be at

1. .3 f
2. 1.5 f
3. .1.5 f
4. 3 f

Answer: 1. .3 f

Question 42. If the critical angle for total internal reflection from a medium to vacuum is 45°, then the velocity of light in the medium is,

1. \(1.5 \times 10^8 \mathrm{~m} / \mathrm{s}\)
2. \(\frac{3}{\sqrt{2}} \times 10^8\)
3. \(\sqrt{2} \times 10^8 \mathrm{~m} / \mathrm{s}\)
4. \(3 \times 10^8 \mathrm{~m} / \mathrm{s}\)

Answer: 2. \(\frac{3}{\sqrt{2}} \times 10^8\)

Question 43. The power of a biconvex lens is 10 dioptre and the radius of curvature of each surface is 10 cm. Then the refractive index of the material of the lens is,

1. \(\frac{4}{3}\)
2. \(\frac{9}{8}\)
3. \(\frac{5}{3}\)
4. \(\frac{3}{2}\)

Answer: 4. \(\frac{3}{2}\)

Question 44. A ray is an incident at an angle of incidence I on one surface of a small angled prism (with the angle of prism A) and emerges normally from the opposite surface. If the refractive index of the material of the prism is μ, then the angle of incidence is nearly equal to

1. \(\frac{\mu A}{2}\)
2. \(\frac{A}{2 \mu}\)
3. \(\frac{2 A}{\mu}\)
4. \(\mu A\)

Answer: 4. \(\mu A\)

Question 45. A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since

1. A large aperture contributes to the quality and visibility of the images
2. A large area of the objective ensures better light-gathering power
3. A large aperture provides a better resolution
4. All of the above.

Answer: 4. All of the above.

Question 46. A convex lens ‘A’ of focal length 20 cm and a concave lens ‘B’ of focal length 5 cm are kept along the same axis with a distance ‘d’ between them. If a parallel beam of light falling on ‘A’ leaves ‘B’ as a parallel beam, then the distance ‘d’ in cm will be

1. 15
2. 50
3. 30
4. 25

Answer: 1. 15

Question 47. Find the value of the angle of emergence from the prism. The refractive index of the glass is √3.

1. 30°
2. 45°
3. 90°
4. 60°

Answer: 4. 60°

Question 48. A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of

1. 30 cm from the lens, it would be a real image
2. 30 cm from the plane mirror, it would be a virtual image
3. 20 cm from the plane mirror, it would be a virtual image
4. 20 cm from the lens, it would be a real image

Answer: 4. 20 cm from the lens, it would be a real image

Question 49. A transparent solid cylindrical rod has a refractive index of \(\frac{2}{\sqrt{3}}\). It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure

1. \(\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)\)
2. \(\sin ^{-1}\left(\frac{2}{\sqrt{3}}\right)\)
3. \(\sin ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)
4. \(\sin ^{-1}\left(\frac{1}{2}\right)\)

Answer: 3. \(\sin ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)

Question 50. A car is fitted with a convex side-view mirror of a focal length of 20 cm. A second car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is:

1. 1/10 m/s
2. 1/15 m/s
3. 10 m/s
4. 15 m/s

Answer: 2. 1/15 m/s

Question 51. A beaker contains water up to a height h₂ and kerosene of height h above water so that the total height of (water + kerosene) is (h₁ + h₂). The refractive index of water is μ₁ and that of kerosene is μ₂. The apparent shift in the position of the bottom of the beaker when viewed from above is:

1. \(\left(1+\frac{1}{\mu_1}\right) \quad \mathrm{h}_1-\left(1+\frac{1}{\mu_2}\right) \mathrm{h}_2\)
2. \(\left(1-\frac{1}{\mu_1}\right) \mathrm{h}_1+\left(1-\frac{1}{\mu_2}\right) \mathrm{h}_2\)
3. \(\left(1+\frac{1}{\mu_1}\right) \quad \mathrm{h}_2-\left(1+\frac{1}{\mu_2}\right) \mathrm{h}_1\)
4. \(\left(1-\frac{1}{\mu_1}\right) \quad \mathrm{h}_2+\left(1-\frac{1}{\mu_2}\right) \mathrm{h}_1\)

Answer: 2. \(\left(1-\frac{1}{\mu_1}\right) \mathrm{h}_1+\left(1-\frac{1}{\mu_2}\right) \mathrm{h}_2\)

Question 52. When monochromatic red light is used instead of blue light in a convex lens, its focal length will:

1. Increase
2. Decrease
3. Remain same
4. Does not depend on the color of the light

Answer: 1. Increase

Question 53. An object 2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1 cm thick, with a refractive index of 1.50 is interposed between lens and film with its plane faces parallel to the film. At what distance (from the lens) should the object be shifted to be in sharp focus on the film?

1. 7.2 m
2. 2.4 m
3. 3.2 m
4. 5.6 m

Answer: 4. 5.6 m

Question 54. The diameter of a plano-convex lens is 6 cm and the thickness at the center is 3 mm. If the speed of light in the material of the lens is 2 x 10⁸ m/s, the focal length of the lens is:

1. 15 cm
2. 20 cm
3. 30 cm
4. 10 cm

Answer: 3. 30 cm

Question 55. The graph between the angle of deviation (δ) and angle of incidence (i) for a triangular prism is represented by :

Answer: 3

Question 56. A thin convex lens made from crown glass \(\left(\mu=\frac{3}{2}\right)\) has focal length f. When it is measured in two different liquids having refractive indices 4/3 and 5/3, it has the focal lengths f₁ and f₂ respectively. The correct relation between the focal length is:

1. f₁ = f₂ > f
2. f₁ > f and f₂ becomes negative
3. f₂ > f and f₁ becomes negative
4. f₁ and f₂ both become negative

Answer: 2. f₁ > f and f₂ becomes negative

Question 57. A green light is incident from the water to the air-water interface at the critical angle (θ). Select the correct statement.

1. The entire spectrum of visible light will come out of the water at an angle of 90° to the normal.
2. The spectrum of visible light whose frequency is less than that of green light will come out of the air medium.
3. The spectrum of visible light whose frequency is more than that of green light will come out to the air medium.
4. The entire spectrum of visible light will come out of the water at various angles to the normal.

Answer: 2. The spectrum of visible light whose frequency is less than that of green light will come out of the air medium.

Question 58. Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is μ, a ray, incident at an angle θ, on the face AB would get transmitted through the face AC of the prism provided:

1. \(\theta>\sin ^{-1}\left[\mu \sin \left(A-\sin ^{-1}\left(\frac{1}{\mu}\right)\right)\right]\)
2. \(\theta<\sin ^{-1}\left[\mu \sin \left(A-\sin ^{-1}\left(\frac{1}{\mu}\right)\right)\right]\)
3. \(\theta>\cos ^{-1}\left[\mu \sin \left(A+\sin \left(\frac{1}{\mu}\right)\right)\right]\)
4. \(\theta<\cos ^{-1}\left[\mu \sin \left(A+\sin \left(\frac{1}{\mu}\right)\right)\right]\)

Answer: 1. \(\theta>\sin ^{-1}\left[\mu \sin \left(A-\sin ^{-1}\left(\frac{1}{\mu}\right)\right)\right]\)

Question 59. An observer looks at a distant tree of height 10 m with a telescope with a magnifying power of 20. To the observer, the tree appears:

1. 10 times nearer
2. 20 times taller
3. 20 times nearer
4. 10 times taller

Answer: 3. 20 times nearer

Question 60. In an experiment for determination of the refractive index of a glass of a prism by i – δ, plot, it was found that a ray incident at angle 35°, suffers a deviation of 40° and that it emerges at angle 79°. In that case which of the following is closest to the maximum possible value of the refractive index?

1. 1.6
2. 1.7
3. 1.8
4. 1.5

Answer: 4. 1.5

Question 61. A diverging lens with a magnitude of focal length 25cm is a converging lens of a magnitude of focal length 20 cm. A beam The final image formed is:

1. Real and at a distance of 6 cm from the convergent lens
2. Real and at a distance of 40 cm from the convergent lens.
3. Virtual and at a distance of 40 cm from the convergent lens
4. Real and at a distance of 40 cm from the divergent lens.

Answer: 2. Real and at a distance of 40 cm from convergent lens.

Question 62. Consider a tank made of glass with a thick bottom. It is filled with a liquid of refractive index μ. A student finds that, irrespective of what the incident angle i (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of μ is:

1. \(\frac{5}{\sqrt{3}}\)
2. \(\frac{4}{3}\)
3. \(\frac{3}{\sqrt{5}}\)
4. \(\sqrt{\frac{5}{3}}\)

Answer: 3. \(\frac{3}{\sqrt{5}}\)

Question 63. A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp image again,, the screen is shifted by a distance d. Then d is:

1. 1.1 cm away from the lens
2. 0.55 cm away from the lens
3. 0.55 cm towards the lens
4. 0

Answer: 2. 0.55 cm away from the lens

Question 64. Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror (M₁) and parallel to the second mirror (M₂) is finally reflected from the second mirror (M₂) parallel to the first mirror (M₁). The angle between the two mirrors will be:

1. 75°
2. 90°
3. 45°
4. 60°

Answer: 4. 60°

Question 65. A plano-convex lens of refractive index μ₁ and focal length f₁ is kept in contact with another plano-convex lens of refractive index μ₂ and focal length f₂. If the radius of curvature of their spherical faces is R each and f₁ = 2f₂, then μ₁ and μ₂ are related as:

1. 2μ₁ – μ₂ = 1
2. μ₁ + μ₂ = 3
3. 3μ₂ – 2μ₁ = 1
4. 2μ₂ – μ₁ = 1

Answer: 1. 2μ₁ – μ₂ = 1

Question 66. The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of the cornea (7.8 mm). This surface separates two media of refractive indices 1 and 1.34. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus:

1. 4.0 cm
2. 2 cm
3. 1 cm
4. 3.1 cm

Answer: 4. 3.1 cm

Question 67. The variation of the refractive index of a crown glass thin prism with a wavelength of incident light is shown. Which of the following graphs is the correct one, if Dm is the angle of minimum deviation?

Answer: 1

Question 68. An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s, the speed and direction of the image will be:

1. 0.92 x 10^-3 m/s away from the lens
2. 3.22 x 10^-3 m/s towards the lens
3. 1.16 x 10^-3 m/s towards the lens
4. 2.26 x 10^-3 m/s away from the lens

Answer: 3. 1.16 x 10^-3 m/s towards the lens

Question 69. A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is √3, then the angle of incidence is:

1. 30°
2. 90°
3. 60°
4. 45°

Answer: 3. 60°

Question 70. What is the position and nature of the image formed by the lens combination shown in the figure? (f₁, f₂ are focal lengths)

1. 70 cm from point B at left; virtual
2. 70 cm from point B at right; real 20
3. 40 cm from point B at right; real
4. 20/3 cm from point B at right, real 3

Answer: 2. 70 cm from point B at right; real 20

Question 71. A point source of light S is placed at a distance L in front of the center of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance of 2L as shown below. The distance over which the man can see the image of the light source in the mirror is:

1. d
2. 3d
3. d/2
4. 2d

Answer: 2. 3d

Question 72. The formation of a real image using a biconvex lens is shown below:

1. Erect real image
2. No change
3. Image disappears
4. Magnified image

Answer: 3. Image disappears

Question 73. A plano-convex lens (focal length f₂, refractive index μ₂, radius of curvature R) fits exactly into a planoconcave lens (focal length f₁, refractive index μ₁, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be:

1. \(\frac{R}{\mu_2-\mu_1}\)
2. \(f_1-f_2\)
3. \(\frac{2 f_1 f_2}{f_1+f_2}\)
4. \(f_1+f_2\)

Answer: 1. \(\frac{R}{\mu_2-\mu_1}\)