PhysicsCBSE Class 12 · Sample paper, session 2025-26 · 5 marks · Long answer

CBSE Class 12 Physics sample paper 2025-26: question 32(II)

From the official CBSE sample question paper for 2025-26, section E, question 32(II), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(II) · 5 marks · Long answerRay Optics and Optical Instruments

(A) Define angle of deviation in a prism?
(B) Obtain the relation $A + δ = i + e$ for a prism where A is the angle of prism, δ is the angle of deviation, i is the angle of incidence and e is the angle of emergence. Write this relation for the minimum deviation?
(C) Write the condition for minimum deviation.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Draw the normals at both faces and look at the quadrilateral and triangle they form with the prism's vertex.

Hint 2

The total deviation is the sum of the deviations at the two faces: $(i - r_{1}) + (e - r_{2})$ .

Hint 3

At minimum deviation the path through the prism is symmetric.

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.

(A) The angle of deviation ( $δ$ ) is the angle between the direction of the incident ray and the direction of the emergent ray after it passes through the prism.
1 mark
(B) Set-up. Let ray PQ strike face AB at Q with angle of incidence $i$ and refract at angle $r_{1}$ . It strikes face AC at R with internal angle $r_{2}$ and emerges at angle $e$ . The normals at Q and R meet at N.
- In quadrilateral AQNR, the angles at Q and R are $9 0^{\circ}$ each. So $∠ A + ∠ QN R = 18 0^{\circ}$ .
- In triangle QNR, $r_{1} + r_{2} + ∠ QN R = 18 0^{\circ}$ .
Comparing the two gives $A = r_{1} + r_{2}$ .
1 mark
Deviation. The deviation at the first face is $(i - r_{1})$ and at the second face is $(e - r_{2})$ . So
$δ = (i - r_{1}) + (e - r_{2}) = (i + e) - (r_{1} + r_{2}) = i + e - A$
Hence $A + δ = i + e$ .
1 mark
At minimum deviation, $i = e$ and $r_{1} = r_{2} = r = A /2$ . The relation becomes $A + δ_{m} = 2 i$ , i.e. $i = \frac{A + δ _{m}}{2}$ .
This gives the refractive index of the prism:
$μ = \frac{sin \frac{A + δ _{m}}{2}}{sin \frac{A}{2}}$
1 mark
(C) Condition for minimum deviation:
- The angle of incidence equals the angle of emergence ( $i = e$ ), so $r_{1} = r_{2}$ .
- Equivalently, the refracted ray inside the prism is parallel to its base (symmetric passage of the ray).
1 mark

Answer: (A) Angle between incident and emergent rays; (B) $A + δ = i + e$ , at minimum deviation $A + δ_{m} = 2 i$ ; (C) $i = e$ ( $r_{1} = r_{2}$ ), ray inside the prism parallel to the base

Where the marks are

Correct definition of the angle of deviation (1 mark)
Shows $A = r_{1} + r_{2}$ from the geometry (1 mark)
Shows $δ = i + e - A$ , hence $A + δ = i + e$ (1 mark)
Writes $A + δ_{m} = 2 i$ for minimum deviation (1 mark)
States the condition $i = e$ / ray parallel to the base inside the prism (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 paperSample paper 2025-26: 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 sample paper 2025-26: question 32(II)

Hints

Step-by-step solution

Revise the chapter

More questions from Ray Optics and Optical Instruments