PhysicsCBSE Class 12 · Board exam 2024, set 55/1/1 · 5 marks · Long answer

CBSE Class 12 Physics 2024: question 33(a)

Set in the CBSE Class 12 board exam of 2024, paper 55/1/1, section E, question 33(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33(a) · 5 marks · Long answerRay Optics and Optical Instruments

(i) A ray of light passes through a triangular prism. Show graphically, how the angle of deviation varies with the angle of incidence? Hence define the angle of minimum deviation.
(ii) A ray of light is incident normally on a refracting face of a prism of prism angle A and suffers a deviation of angle $δ$ . Prove that the refractive index n of the material of the prism is given by $n = \frac{s i n ( A + δ )}{s i n A}$ .
(iii) The refractive index of the material of a prism is $2$ . If the refracting angle of the prism is $6 0^{\circ}$ , find the
(1) Angle of minimum deviation, and
(2) Angle of incidence.

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

Hints

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

Hint 1

As the angle of incidence increases, the deviation first falls and then rises.

Hint 2

For normal incidence, the angle inside the glass at the second face equals A. Use δ = e − A.

Hint 3

Use $n = sin \frac{A + δ _{m}}{2} / sin \frac{A}{2}$ and recall that sin 45° = 1/√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) Graph (described in words): Plot the angle of deviation $δ$ (y-axis) against the angle of incidence $i$ (x-axis).
The curve is U-shaped. As $i$ increases, $δ$ first decreases to a minimum value $δ_{m}$ , and then increases again. The lowest point of the curve is marked $δ_{m}$ .
1 mark
Angle of minimum deviation $δ_{m}$ is the smallest deviation produced by the prism. At this position, the angle of incidence equals the angle of emergence ( $i = e$ ), and the refracted ray inside the prism travels parallel to the base.
1 mark
(ii) Normal incidence on the first face means $i = 0$ and $r_{1} = 0$ . Since $r_{1} + r_{2} = A$ , the ray meets the second face at an angle $r_{2} = A$ .
The total deviation is $δ = (i - r_{1}) + (e - r_{2}) = e - A$ , so $e = A + δ$ .
Applying Snell's law at the second face (glass to air):
$n sin A = 1 \cdot sin (A + δ) \Rightarrow n = \frac{sin ( A + δ )}{sin A}$
1 mark
(iii)(1) Use $n = \frac{sin \frac{A + δ _{m}}{2}}{sin \frac{A}{2}}$ :
$2 = \frac{sin \frac{6 0 ^{\circ} + δ _{m}}{2}}{sin 3 0 ^{\circ}}$
$\Rightarrow sin \frac{6 0 ^{\circ} + δ _{m}}{2} = \frac{2}{2} = \frac{1}{2} = sin 4 5^{\circ}$
$\frac{6 0 ^{\circ} + δ _{m}}{2} = 4 5^{\circ} \Rightarrow δ_{m} = 3 0^{\circ}$
1 mark
(2) At minimum deviation, $i = \frac{A + δ _{m}}{2} = \frac{6 0 ^{\circ} + 3 0 ^{\circ}}{2} = 4 5^{\circ}$
1 mark

Answer: (i) U-shaped δ–i curve; δ_m occurs when i = e; (ii) n = sin(A+δ)/sin A proved; (iii)(1) δ_m = 30°, (2) i = 45°

Where the marks are

Correct δ versus i graph showing a minimum (1 mark)
Definition of angle of minimum deviation (i = e / ray parallel to base) (1 mark)
Proof using r₂ = A, e = A + δ and Snell's law at the second face (1 mark)
δ_m = 30° from the prism formula (1 mark)
i = 45° (1 mark)

Revise the chapter

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 55/1/1: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 12 Physics 2024: question 33(a)

Hints

Step-by-step solution

Revise the chapter

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