## Optics

## Refraction Of Light Multiple Choice Questions

**Question 1. A rectangular block of glass ABCD has A p a refractive index 1.6. A pin is placed midway When observed from the face AD, the pin shall**

- Appears to be near A
- Appears to be near D
- Appear to be at the centre of AD
- Not be seen at all

**Answer:** 4. not be seen at all

**Question 2. You are given four sources of light each one providing a light of single colour—red, blue, green and yellow. Suppose the angle of refraction for a beam of yellow light corresponding to a particular angle of incidence at the interface of two media is 90°. Which of the following statements is correct if the source of the yellow light is replaced with other lights without changing the angle of incidence? **

- The beam of red light would undergo total internal reflection
- The beam of red light would bend towards the normal while it gets refracted through the second medium
- The beam of blue light would undergo total internal reflection
- The beam of green light would bend away from the normal as it gets refracted through the second medium

**Answer:** 3. The beam of blue light would undergo total internal reflection

**Read and Learn More Class 12 Physics Multiple Choice Questions**

**Question 3. An extended object kept underwater in a deep container appears distorted when seen from near the edge of the container. It so happens because**

- The apparent depth of the points near the edge is less than that of the points away from the edge
- The angle subtended by the object when submerged in water is less than that when the object is in air
- Some points away from the edge undergo total internal reflection and become invisible
- The water in the container acts as a lens and enlarges the object

**Answer:** 1, 2 And 3

**Question 4. If C _{1} and C_{2 }are medium respectively, then the relation of the velocity of light with the refractive index of the medium will be the velocities of light in a vacuum and in a**

- \(\mu=\frac{c_1}{c}\)
- mu = c1c
- \(\mu=\frac{c}{c_1}\)
- μ= C
_{1 }-C_{2}

**Answer:** 3 . \(\mu=\frac{c}{c_1}\)

**Question 5. When light moves from glass to air, the property of which remains unchanged is**

- Velocity
- Wavelength
- Frequency
- Amplitude

**Answer:** 3. Frequency

**Question 6. The refractive indices of a medium for two light waves are μ _{1 }and μ_{2} = If μ_{1 }>μ_{2} then which wave will move faster in the medium?**

- First wave
- Second wave
- The two waves will move with the same velocity
- Cannot be said correctly

**Answer:** Second wave

**Question 7. The refractive index of a medium in which the velocity of light is \(2 \times 10^8 \mathrm{~m} \cdot \mathrm{s}^{-1}\) is **

- 1.4
- 2.3′
- 1.5
- 1.0

**Answer:** 3. 1.5

**Question 8. Wavelength, frequency, velocity and intensity of light when travelling in air is λ, ν, v and I respectively. When the light ray enters the water the values of the above-mentioned properties λ _{1}, ν_{1}, v_{1} become I_{1} and ly respectively. Which relation is correct**

- λ = λ
_{1} - ν= ν
_{1} - v= v
_{1} - I= I
_{1}_{ }

**Answer:** 2. ν= ν_{1}

**Question 9. In case of refraction of light which of the following phenomena must take place?**

- Change of direction
- Change of velocity
- Both 1and 2
- None of 1,2,3

**Answer:** 2. Change of velocity

**Question 10. If the refractive indices of a particular medium for red and violet light be and respectively, then**

- μ
_{r }>μ_{v} - μ
_{r }<μ_{v} - μ
_{r }= μ_{v} - None of these

**Answer:** 2. μ_{r }<μ_{v}

**Question 11****. Speed of light through two media of refractive indices and are and respectively**

- u
_{1}= u_{1} - n
_{1}u_{1 }= n_{2}u_{2} - n
_{1}u_{2 }= n_{2}u_{1} - n
_{1}u²_{1 }= n_{2}u²_{2}

**Answer: ** n_{1}u_{1 }= n_{2} u_{2}

Deviation of a Ray of Light

**Question 12. In the case of refraction, angle of deviation is maximum when the angle of incidence is**

- 45°
- 0°
- 90°
- 60°

**Answer:** 3.90°

**Question 13. In the case of refraction, the angle of deviation becomes minimum when the angle of incidence becomes**

- 45°
- 0°
- 90°
- 60°

**Answer: **2. 0°

**Question 14. A diverging beam of rays from a point source S, making a divergent angle, a are incident on a glass slab The angle of incidence of the extreme rays on the two sides is the same. If the thickness of the glass slab is t and the refractive index n, then the E angle of divergence of the emergent rays will be**

- Zero
- α
- \(\sin ^{-1} \frac{1}{n}\)
- 2 \(\sin ^{-1} \frac{1}{n}\)

**Answer:** 2.α

**Question 15. A ray of light is incident on the upper surface of a glass plate of thickness t (fx refractive index of glass). If the angle of incidence i is very small, then the lateral displacement of the emergent ray will be**

- \(\frac{t i \mu}{\mu+1}\)
- \(\frac{t i(\mu-1)}{\mu}\)
- \(\frac{t i \mu}{\mu-1}\)
- \(\frac{t i(\mu+1)}{\mu}\)

**Answer:** 2 \(\frac{t i(\mu-1)}{\mu}\)

**Question 16. A fight ray travels through four adjacent media of refractive μ _{1 } ,μ_{2}, μ_{3} ,μ_{4} indices the bases of the media are parallel if emergent to the incident ray AB Then**

- μ
_{1 }= μ_{2} - μ
_{2 }= μ_{3} - μ
_{3 }= μ_{4} - μ
_{4 }= μ_{1}

**Answer:** 4. μ_{4 }= μ_{1}

**Question 17. Two rays of light are incident normally on die surface of the water \(\frac{4}{3}\). The refractive index of water is|. A glass box is kept j inside the water whose height is h. A ray passes through the box and touches the bottom. The rays 1 and 2 touch the bottom at a time gap of \h’ – height from the top of the glass to the surface of the water; c = speed of light]**

- 0
- \(\frac{h^{\prime}}{6 c}\)
- \(\frac{h}{6 c}\)
- \(\frac{6 h}{c}\)

**Answer: ** 1. 0

**Question 18. Let the XZ plane be the boundary between two transparent media. Medium 1 in Z≥0 has a refractive index of \(\sqrt{2}\) and medium with 2 Z<0 has a refractive index of \(\sqrt{3}\) a ray of light in medium 1 given by the vector A = 6\(\sqrt{3}\)i+8\(\sqrt{2}\) j + 10k incident on the plane of separation. The angle of refraction in medium 2 is**

- 45°
- 60°
- 75°
- 30°

**Answer:** 1. 45°

**Question 19. The refractive indices of a rarer and a denser medium are** **μ**_{1 }**and μ _{2 }respectively. The apparent depth of an object, placed in a rarer medium, to an observer situated in a denser medium will be**

- \(\frac{\mu_2}{\mu_1}\)
- \(\frac{\mu_1}{\mu_2}\)
- \(\frac{\mu_1}{\mu_2} \times \text { real depth }\)
- \(\frac{\mu_2}{\mu_1} \times \text { real depth }\)

**Answer:** 4. \(\frac{\mu_2}{\mu_1} \times \text { real depth }\)

**Question 20. There is a point object at the centre of a glass sphere of diameter 12 cm and a refractive index of 1.5. The distance of the virtual image from the surface of the sphere is**

- 4 cm
- 6 cm
- 9 cm
- 12 cm

**Answer:** 2. 6 cm

**Question 21. A rectangular glass slab is placed on different alphabets written in different colours. The coloured alphabet which appears to have been raised minimum in comparison with other alphabets is**

- Blue
- Violet
- Green
- Red

**Answer:** 4. Red

**Question 22. A container of depth 2d is half-filled with a liquid of refractive index \(\sqrt{2}\) and another half with a liquid of refractive indexμ. The two liquids do not mix with each other. The apparent depth of the inner surface of the bottom of the container will be (neglect the thickness of the bottom of the container)**

- \(\frac{\mu}{d(\mu+2)}\)
- \(\frac{d(\mu+\sqrt{2})}{\mu \sqrt{2}}\)
- \(\frac{\sqrt{2} \mu}{d(\mu+\sqrt{2})}\)
- \(\frac{\mu d}{d+3 \mu}\)

**Answer:** 2. \(\frac{d(\mu+\sqrt{2})}{\mu \sqrt{2}}\)

**Question 23. To a fish underwater, viewing obliquely a fisherman standing on the bank of a lake, the man looks**

- Taller than what he actually is
- Shorter than he actually is
- The same height as he actually is
- Depends on the obliquity

**Answer: **1. Taller than what he actually is

**Question 24. A transparent cube of 0.21 m edge contains a small air bubble. Its apparent distances when viewed through one face of the cube is 0.10 m and when viewed from the opposite face is 0.04 m. The actual distance of the bubble from the second face of the cube is**

- 0.06 m
- 0.17 m
- 0.05 m
- 0.04 m

**Answer:** 1. 0.06 m

**Question 25. in a rectangular glass container five different immiscible transparent liquids A, B, C, D, E are kept according to their respective densities, layerwise. In refractive indices of each liquid has been given. The container is illuminated from one side. A very small piece of glass {fi = 1.61) is gradually dropped into the vessel. During its fall through the layers, the glass piece will become invisible in**

- Liquids A and B
- The liquid C
- Liquids D and E
- All the liquids— A, B, C, D, E

**Answer: 2. ** The liquid C

**Question 26. A lens of a refractive index 1.5 is kept in a medium of refractive index 1.5. The refractive index ofthe lens with respect to the medium will be**

- 1.5
- 1.5 ×1.5
- 1
- 1.5 + 1.5

**Answer:** 3.1

**Question 27. If a ray of light is incident normally on any face of an equi¬ lateral glass prism, then the ray will deviate through an angle**

- 30°
- 60°
- 90°
- 120°

**Answer: **1.30°

**Question 28. A ray of light is passed from an optically denser medium to a rarer medium. The critical angle for the pair of media is C. The maximum angle of deviation of the ray will be**

- π – C
- \(\frac{\pi}{2}-C\)
- 2C
- \(\frac{\pi}{2}+C\)

**Answer:** 2. \(\frac{\pi}{2}-C\)

**Question 29. Critical angle depends on**

- Colour of light
- Refractive indices of the two concerned media
- Colour of light and refractive indices of the two concerned media
- Wavelength of light

**Answer:** 2. Colour of light and refractive indices of the two concerned media

**Question 30. A ray of light is incident normally on one face of a right-angled isosceles prism. It then grazes the hypotenuse. The refractive index of the material of the prism is**

- 1.33
- 1. 414
- 1.5
- 1.732

**Answer:** 2. 1. 414

**Question 31. Light rays from a point source situated at a depth of h below water can emerge in air through a definite circular section. If the refractive index of water is , the value of the radius of the circular section will be**

- \(\frac{\sqrt{7}}{3} h\)
- \(\frac{3}{\sqrt{7}} h\)
- \(\frac{\sqrt{3}}{7} h\)
- \(\frac{7}{\sqrt{3}} h\)

**Answer:** 2. \(\frac{3}{\sqrt{7}} h\)

**Question 32. 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. What is the velocity of the light in the liquid?**

- \(1.8 \times 10^8 \mathrm{~m} \cdot \mathrm{s}^{-1}\)
- \(2.4 \times 10^8 \mathrm{~m} \cdot \mathrm{s}^{-1}\)
- \(3.0 \times 10^8 \mathrm{~m} \cdot \mathrm{s}^{-1}\)
- \(1.2 \times 10^8 \mathrm{~m} \cdot \mathrm{s}^{-1}\)

**Answer: **1. \(1.8 \times 10^8 \mathrm{~m} \cdot \mathrm{s}^{-1}\)

**Question 33. How does the surface of water appear to the eye of an observer inside water?.**

- Mirror with a circular hole
- Mirror with an elliptical hole
- Mirror without hole
- Mirror with a square hole

**Answer:** 1. Mirror with a circular hole

**Question 34. A fish looking up through the water sees the outside world, contained in a circular horizon. If the refractive index of water is \(\frac{4}{3}\)and the fish is 12 cm below the water surface, then the radius of this circle in cm is**

- \(36 \sqrt{7}\)
- \(\frac{36}{\sqrt{7}}\)
- \(36 \sqrt{5}\)
- \(4 \sqrt{5}\)

**Answer: ** 2. \(\frac{36}{\sqrt{7}}\)

**Question 35. When a light ray travels from one medium to another and gets refracted, the velocity of light becomes doubled. For total internal reflection in this condition, the value of the critical angle is**

- 30°
- 90°
- 60°
- Cannot be determined

**Answer:** 1. 30°

**Question 36. Light is incident normally on the side AB of a right-angled prism ABC made of glass. A liquid of refractive index j-t is kept above the side AC. The refractive index of the material of 3 the prism is -. What is the value of μ for which there will be a total internal reflection on AC?**

- \(\mu>\sqrt{3}\)
- \(\mu<\frac{\sqrt{3}}{2}\)
- \(\mu<\frac{3 \sqrt{3}}{4}\)
- \(\mu>\frac{\sqrt{3}}{2}\)

**Answer:** 3. \(\mu<\frac{3 \sqrt{3}}{4}\)

**Question 37. The length of a day due to atmospheric refraction**

- Decreases
- Increased
- Remains unchanged
- Sometimes decreases

**Answer:** 2. Increased

**Question 38. The twinkling effect of starlight Is due to**

- Total internal reflection
- High-dense matter of star
- Constant burning of hydrogen In the star
- The fluctuating apparent position of the star is slightly different from the actual position of the star

**Answer:** 4. The fluctuating apparent position of the star is slightly different from the actual position of the star

**Question 39. The refractive angle of a prism is 60°. If the prism Is immersed in a liquid then the minimum angle of deviation is 30°. Critical angle of glass with respect to the liquid Is**

- 42°
- 45°
- 50°
- 52°

**Answer:** 2. 45°

**Question 40. A ray of light passes through an isosceles triangle such that the angle of incidence is equal to the angle of emergence. If the angle of emergence and angle of Incidence are both 45° then the angle of deviation will be**

- 15°
- 75°
- 90°
- 150°

**Answer:** 4. 150°

**Question 41. The refractive index of a prism is \(\sqrt{2}\) and its refractive angle is 60° . If a ray emerges with the minimum angle of deviation then the angle of incidence will be**

- 45°
- 60°
- 90°
- 150°

**Answer:** 1. 45°

**Question 42. A ray of light PQ is incident on the face of an isosceles glass prism kept on a horizontal table. If for the ray PQ the prism is at the position of minimum deviation then**

- α = β
- α > β
- α < β
- α + β = 90

**Answer: ** 1. α = β

**Question 43. The angle of deviation for a thin prism of refractive index 1.5 is 4° for an incident ray. If that prism is dipped in water, then for the same incident ray, the angle of deviation would be \(\text { given } \left.\mu_{\text {water }}=\frac{4}{3}\right]\) **

- 1°
- 2°
- 8°
- 16°

**Answer:** 1. 1°

**Question 44. A thin prism of angle 15° made of glass of refractive index in glass? μ _{12}= 1.5 is combined with another prism of a glass of refractive index μ_{2} = 1-75. The combination of the prisms produces dispersion without deviation, The angle of the second prism should be**

- 5°
- 7°
- 10°
- 12°

**Answer:** 3. 10°

**Question 45. A monochromatic beam of light of wavelength λ and frequency f travelling In a vacuum enters a diamond of refractive Index 2.4 t. Then**

- Its wavelength will reduce to \(\frac{\lambda}{2.4}\)
- Its wavelength will Increase to\(\)
- Its frequency will reduce to \(\frac{f}{2.4}\)
- Its wavelength will Increase to \(\frac{c}{2.4}\)

**Answer:** 1,4

**Question 46. A ray of light travelling in a transparent medium falls on a surface separating the medium front air at an angle of Indeuce of 45°. The ray undergoes total (internal reflection. If H Is the refractive Index of the medium with respect to atr, select the possible values) of ft from the following**

- 1.3
- 1.4
- 1.5
- 1.6

**Answer: ** 3,4

**Question 47. For a light ray pawing through a given prism**

- If the angle of incidence is increased, the deviation Increases
- If the die angle of Incidence is decreased, the deviation increases
- If the angle of Incidence is either Increased or decreased hum a certain value, the deviation Increases
- The angle of minimum deviation Is directly piupnttlonal to the angle of the prism if the prism Is thin

**Answer:** 3,4

**Question 48. A bird flies down vertically towards a water surface. To a fish inside the water, vertically below the bird, the bird will appear to**

- Be farther away than its actual distance
- Be closer than its actual distance
- Move faster than its actual speed
- Move slower than its actual speed

**Answer: ** 1,3

**Question 49. The refractive index of the material of an equilateral prism is \(\sqrt{2}\)**

- For a ray of light, the minimum angle of deviation is 30°
- For a ray of light, the minimum angle of deviation is 45°
- At a 45° angle of incidence, the deviation of a ray becomes the minimum
- At 60° angle of incidence, the deviation of a ray becomes minimum

**Answer: ** 1,3

**Question 50. In a vacuum, the speed of light is ν _{0}, frequency is n and wavelength is n_{0}. When a ray travels from one medium to another, the above physical quantities become ν, n and λ respectively, μ is the refractive index of the medium. Which of the following statements is correct?**

- \(n=\frac{n_0}{\mu}\)
- \(\lambda=\frac{\lambda_0}{\mu}\)
- \(v=\frac{v_0}{\mu}\)
- n = n
_{0}

**Answer:** 2,3, and 4

**Question 51. The refractive indices of three media 1,2, and 3, are (μ _{1}, μ_{2}, and μ_{3)}, respectively Which of the following statements is correct?**

- Total internal reflection of light ray takes place when it travels from medium 3 to 1
- The value of the critical angle for refraction of light when it travels from medium 1 to 2 is less than that when it travels from medium 1 to 3
- The value of critical angle for refraction of light when it travels from medium 1 to 2 is more than that when it travels from medium 1 to 3
- The possibility of total internal reflection is more when light ray travels from medium 1 to 3 than when it travels from medium 1 to 2

**Answer:** 1,3 and 4

**Question 52. A monochromatic ray of light is incident normally on a refracting face of a prism of angle 30° . The refractive index of the material of the prism is 1.5.**

**1. The angle of emergence will be**

- 32.5°
- 20.6°
- 48.6°
- 18.6°

**Answer:** 3. 48.6°

**2. The angle of deviation will be**

- 32.5°
- 20.6°
- 48.6°
- 18.6°

**Answer:** 4. 18.6°

**Question 53. The refractive index ofthe material ofa prism is J? and the refracting angle is 90° .**

**1. The angle of minimum deviation of the refracted ray by the prism is**

- 30°
- 35
- 40°
- 45°

**Answer:** 1. 30°

**2. The corresponding incidence is**

- 30°
- 35°
- 40°
- 60°

**Answer: ** 4. 60°

**3. The limiting angle of incidence for emergent ray is**

- 30°
- 45°
- 50°
- 60°

**Answer:** 2. 45°

**Question 54. A glass slab consists of thin uniform layers of progressively decreasing refractive indices such that the refractive index ofany layer is (i- mA/i. Here fi and Afi denote the refractive index of the 0 th layer and the difference in refractive index sinr sin(90°-/) between any two consecutive layers respectively. The integer m = 0, 1, 2, 3, denotes the numbers of the successive layers. A ray oflight from the 0 th layer enters the 1st layer at an angle of incidence of 30°. After undergoing the m th refraction, the ray emerges parallel to the interface. If μ= 1-5 and Δμ = 0.015 the value of m is**

- 20
- 30
- 40
- 50

**Answer:** 4. 50

From Snell’s law, we have, for n number of media,

Or,\(\frac{3}{2} \times \frac{1}{2}=(1.5-m \times 0.015) \times 1\)

\(0.015 m=\frac{3}{4}\)m = \(\frac{3}{4} \times \frac{1000}{15}\)

= 50

**Question 55. A ray of light is incident at an angle i on a glass slab of refractive index μ . The angle between reflected and refracted light is 90° . Then the relationship between i and μ is.**

- i = tan-1 (\(\left(\frac{1}{\mu}\right)\)
- tan i= μ
- sin i = μ
- cos i = μ

**Answer:** 2. tan i= μ

According to

i+ 90+r = 180

Or, r= 90- i

Refractive index = \(\)

= tan i

**Question 56. When light is refracted from a surface, which ofits following physical parameters does not change?**

- Velocity
- Amplitude
- Frequency
- Wavelength

**Answer: ** 3. Frequency

When light is refracted from a surface, frequency is the physical parameter that does not change

**Question 57. A ray of light strikes a glass plate at an angle of 60°. reflected and refracted rays are perpendicularto each other, the refractive index ofglass is**

- \(\frac{\sqrt{3}}{2}\)
- \(\frac{3}{2}\)
- \(\frac{1}{2}\)
- \(\sqrt{3}\)

**Answer:** 4. \(\sqrt{3}\)

According to the question, i= 60°

Hence i+90°+r= 180°

Or, 60°+90°+r= 180°

r = 30°

∴ \(\frac{\sin i}{\sin r}=\mu\)

Or, \(\frac{\sin 60^{\circ}}{\sin 30^{\circ}}=\mu\)

Or, \(\sqrt{3}\)

**Question 58. Light travels through a glass plate of thickness t and having refractive index μ. If c is the velocity of light in a vacuum, time taken by the light to travel through this thickness of the glass is**

- \(\frac{t}{\mu c}\)
- \(\frac{t c}{\mu}\)
- \(\frac{\mu t}{c}\)
- μtc

**Answer:** 3. \(\frac{\mu t}{c}\)

Required time = \(=\frac{\text { thickness of the slab }}{\text { velocity of light in the slab }}\)

= \(\frac{t}{c}=\frac{\mu t}{c}\)

**Question 59. Monochromatic light is incident on a glass prism of angle A. If the refractive index ofthe material of the prism is μ , a ray, incident at an angle θ, on the face PQ would get transmitted through the face PR ofthe prism provided.**

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

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

We know \(i_1=\sin ^{-1}\left(\sin A \sqrt{\mu^2-1}-\cos A\right)\)

Here, i_{1}=θ

Now \(\sqrt{\mu^2-1}-\cos A=\mu\left(\sin A \frac{\sqrt{\mu^2-1}}{\mu}-\cos A \frac{1}{\mu}\right)\)

Where B= \(\sin ^{-1}\left(\frac{1}{\mu}\right)=\cos ^{-1} \frac{\sqrt{\mu^2-1}}{\mu}\)

= \(\mu \sin (A-B)=\mu \sin \left(A-\sin ^{-1} \frac{1}{\mu}\right)\)

The required condition is θ≥ sin^{-1} \(\left[\mu \sin \left(A-\sin ^{-1}\left(\frac{1}{\mu}\right)\right)\right]\)

**Question 60. In an experiment for determination of the refractive index of glass of prism by i-δ, plot, it was found that a ray incident sin ^{-1} 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 ofthe refractive index**

- 1.5
- 1.6
- 1.7
- 1.8

**Answer: ** 1. 1.5

We know, θ = i + e- A

or, 40° = 35° 4- 79° -A or, A = 74 e

Now, the minimum value of the angle of deviation, 8m < 40°

In that case , μ≤ \(\frac{\sin \left(\frac{A+\delta m}{2}\right)}{\sin \frac{A}{2}}\)

Or, μ≤\(\frac{\sin \left(\frac{74^{\circ}+40^{\circ}}{2}\right)}{\sin \frac{74^{\circ}}{2}}\)

Or, 1.39

= 1.5

**Question 61. The angle of a prism is A. One of its refracting surfaces Is silvered. Light rays falling at an angle of incidence 2A on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index μ, of the prism, is**

- 2 sin A
- 2 cos A
- \(\frac{1}{2}\) Cos A
- Tan A

**Answer:** 2. 2 sin A

According to Snell’s law,

1. sin 2A = sin A

Refractive Index of the material of the prism,

\(=\frac{\sin 2 A}{\sin A}=\frac{2 \cos A \sin A}{\sin A}\)= 2 cosA

**Question 62. The refracting angle of a prism is A, and the refractive index of the material of the prism is cot(A/2). The angle of minimum deviation is**

- 180°- 3A
- 180°-2A
- 90°- A-B
- 180°+ 2A

**Answer:** 2. 180°-2A

We know \(y=\frac{\sin \frac{A+B_\pi}{2}}{\sin \frac{A}{2}}\)

⇒ \(\sin \frac{A-3 \pi}{2}=p \sin \frac{A}{2}=\cos \frac{A}{2} \sin \frac{A}{2}\)

⇒ cos\(\frac{A}{2}\) = sin(90- \(\frac{A}{2}\)

⇒ \(\frac{A-3}{2} \pi=90^2-\frac{A}{2}\)

**Question 63. The angle of incidence for a ray of light at a refracting surface of a prism is 45 the angle of prism is 60 If the ray suffer minimum deviation through the prism the angle of minimum deviation and refractive index of the material of the prism respectively are:**

- 30, \(\sqrt{2}\)
- 45, \(\sqrt{2}\)
- 30, \(\frac{1}{\sqrt{2}}\)
- 45, \(\frac{1}{\sqrt{2}}\)

**Answer: ** 1. 30, \(\sqrt{2}\)

Minimum Angle of deviation

δ_{m }= 2i – A = 2 × 45° – 60 °= 30°

For minuimu8m deviation r_{1} = \(\frac{A}{2}=\frac{60^{\circ}}{2}\) = 30°

= 30°

For refraction at point p

sin 45 = sin 30°

Or , μ = \(\sqrt{2}\)

**Question 64. If the angle of a prism is 60’ and angle of minimumdeviation is 40’, then the angle of refraction will be**

- 4°
- 30°
- 20°
- 3°

**Answer: **2. 30°

When angle ofdeviation is minimum, the angle of refraction becomes r = \(r\frac{A}{2}\)

r = \(\frac{60^{\circ}}{2}\) = 30

**Question 65. The refractive index ofthe material of a prism is Jl and the angle of the prism is 30’. One of the two refracting surfaces of the prism is made a mirror inwards, by 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 ofincidence on the prism is**

- 30°
- 45°
- 60°
- Zero

**Answer:** 2. 45°

Applying Snells law at point M,

\(\frac{\sin i}{\sin 30^{\circ}}=\frac{\sqrt{2}}{1}\)Or, \(\sqrt{2} \times \frac{1}{2}\)

= \(\frac{1}{\sqrt{2}}\)

i = 45°