A prism is an optical medium bounded by three refracting plane surfaces. A ray of light suffers successive refractions on passing through its two surfaces and deviates by a certain angle from its original path. The refractive index of the material of the prism is given by μ = ((A+ m)/(2) ) / /2. If the angle of incidence on the second surface is greater than an angle called critical angle, the ray will not be refracted from the second surface and is totally internally reflected. (i) The critical angle for glass is θ_1 and that for water is θ_2. The critical angle for glass-water surface would be (given _aμ_g = 1.5, _aμ_w = 1.33) (ii) When a ray of light of wavelength λ and frequency is refracted into a denser medium (iii)(a) The critical angle for a ray of light passing from glass to water is minimum for (iii)(b) Three beams of red, yellow and violet colours are passed through a prism, one by one under the same condition. When the prism is in the position of minimum deviation, the angles of refraction from the second surface are r_R, r_Y and r_V respectively. Then (iv) A ray of light is incident normally on a prism ABC of refractive index √(2), as shown in figure. After it strikes face AC, it will

PhysicsCBSE Class 12 · Board exam 2024, set 55/5/1 · 4 marks · Case-based

CBSE Class 12 Physics 2024: question 30

Set in the CBSE Class 12 board exam of 2024, paper 55/5/1, section D, question 30, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q30 · 4 marks · Case-basedCompetency-basedRay Optics and Optical Instruments

A prism is an optical medium bounded by three refracting plane surfaces. A ray of light suffers successive refractions on passing through its two surfaces and deviates by a certain angle from its original path. The refractive index of the material of the prism is given by $μ = sin (\frac{A + δ m}{2}) / sin \frac{A}{2}$ . If the angle of incidence on the second surface is greater than an angle called critical angle, the ray will not be refracted from the second surface and is totally internally reflected.

(i)
The critical angle for glass is $θ_{1}$ and that for water is $θ_{2}$ . The critical angle for glass-water surface would be (given $_{a} μ_{g} = 1.5$ , $_{a} μ_{w} = 1.33$ )
1. (A)less than $θ_{2}$
2. (B)between $θ_{1}$ and $θ_{2}$
3. (C)greater than $θ_{2}$
4. (D)less than $θ_{1}$
1 mark
(ii)
When a ray of light of wavelength $λ$ and frequency $υ$ is refracted into a denser medium
1. (A) $λ$ and $υ$ both increase.
2. (B) $λ$ increases but $υ$ is unchanged.
3. (C) $λ$ decreases but $υ$ is unchanged.
4. (D) $λ$ and $υ$ both decrease.
1 mark
(iii)(a)
The critical angle for a ray of light passing from glass to water is minimum for
1. (A)red colour
2. (B)blue colour
3. (C)yellow colour
4. (D)violet colour
1 mark
OR
(iii)(b)
Three beams of red, yellow and violet colours are passed through a prism, one by one under the same condition. When the prism is in the position of minimum deviation, the angles of refraction from the second surface are $r_{R}$ , $r_{Y}$ and $r_{V}$ respectively. Then
1. (A) $r_{V} < r_{Y} < r_{R}$
2. (B) $r_{Y} < r_{R} < r_{V}$
3. (C) $r_{R} < r_{Y} < r_{V}$
4. (D) $r_{R} = r_{Y} = r_{V}$
1 mark
(iv)
A ray of light is incident normally on a prism ABC of refractive index $2$ , as shown in figure. After it strikes face AC, it will
1. (A)go straight undeviated
2. (B)just graze along the face AC
3. (C)refract and go out of the prism
4. (D)undergo total internal reflection
1 mark

Figure in the paper: Right-angled triangle ABC with right angle at B, vertex A at top with angle 60°, AB vertical, BC horizontal. A ray falls horizontally from the left, normally on face AB. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 55/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

For a boundary between two media, sin c = μ_rarer/μ_denser.

Hint 2

Which quantity is fixed by the source during refraction?

Hint 3

In (iv), find the angle of incidence on AC from the 60° angle and compare it with the critical angle for μ = √2.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(i) Glass–water: $sin c = \frac{1.33}{1.5} = 0.887$ , so $c \approx 62. 5^{\circ}$ .
For comparison, $θ_{1} = sin^{- 1} \frac{1}{1.5} \approx 41. 8^{\circ}$ and $θ_{2} = sin^{- 1} \frac{1}{1.33} \approx 48. 8^{\circ}$ .
So $c > θ_{2}$ . Option (C).
1 mark
(ii) Frequency is set by the source and does not change on refraction. Speed decreases in the denser medium, so $λ = v / ν$ decreases.
Option (C).
1 mark
(iii)(a) $sin c = \frac{μ _{w}}{μ _{g}}$ . Violet has the largest refractive index in glass relative to water, so its critical angle is the smallest.
Option (D).
(iii)(b) At minimum deviation the emergent angle equals $i$ , and $δ_{m} = 2 i - A$ . Deviation is greatest for violet and least for red, so the angle of emergence (angle of refraction at the second surface) is greatest for violet.
Thus $r_{R} < r_{Y} < r_{V}$ . Option (C).
1 mark
(iv) The ray enters face AB normally and travels undeviated to face AC. With $∠ A = 6 0^{\circ}$ , the angle of incidence on AC is $6 0^{\circ}$ .
Critical angle: $c = sin^{- 1} \frac{1}{2} = 4 5^{\circ}$ .
Since $6 0^{\circ} > 4 5^{\circ}$ , the ray undergoes total internal reflection. Option (D).
1 mark

Answer: (i) C; (ii) C; (iii)(a) D; (iii)(b) C; (iv) D

Where the marks are

(i) greater than θ₂ – C (1 mark)
(ii) λ decreases, ν unchanged – C (1 mark)
(iii)(a) violet – D, or (iii)(b) r_R < r_Y < r_V – C (1 mark)
(iv) total internal reflection – D (1 mark)

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Chapter: Ray Optics and Optical Instruments (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Ray Optics and Optical Instruments, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 55/5/1: every question, by section.

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CBSE Class 12 Physics 2024: question 30

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