(a) State the two conditions under which total internal reflection occurs. (b) A transparent container contains layers of three immiscible transparent liquids A, B and C of refractive indices n, 3/4n and 2/3n, respectively. A laser beam is incident at the interface between A and B at an angle θ as shown in figure. Prove that the beam does not enter region C at all for θ ≥ 2/3.

PhysicsCBSE Class 12 · Board exam 2026, set 55/1/1 · 3 marks · Short answer

CBSE Class 12 Physics 2026: question 28

Set in the CBSE Class 12 board exam of 2026, paper 55/1/1, section C, question 28, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28 · 3 marks · Short answerRay Optics and Optical Instruments

(a) State the two conditions under which total internal reflection occurs.
(b) A transparent container contains layers of three immiscible transparent liquids A, B and C of refractive indices n, $\frac{3}{4}$ n and $\frac{2}{3}$ n, respectively. A laser beam is incident at the interface between A and B at an angle $θ$ as shown in figure. Prove that the beam does not enter region C at all for $sin θ \geq \frac{2}{3}$ .

Figure in the paper: Container with three horizontal liquid layers: bottom A (index n), middle B (index 3n/4), top C (index 2n/3). A laser beam enters from below, incident on the A-B interface at angle θ, then continues into B. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 55/1/1.

Hints

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

Hint 1

Because the layers are parallel, the refraction angle in B is the incidence angle at the B–C interface.

Hint 2

Find the critical angle for going from B into C, then work back to θ using Snell's law at A–B.

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) Total internal reflection occurs when:
(i) light travels from an optically denser medium to an optically rarer medium; and
(ii) the angle of incidence in the denser medium is greater than the critical angle for the pair.
1 mark
(b) At the A–B interface, Snell's law gives $n sin θ = \frac{3}{4} n sin r \Rightarrow sin r = \frac{4}{3} sin θ$ . The interfaces are parallel, so $r$ is the angle of incidence at the B–C interface.
½ mark
Critical angle at the B–C interface (B denser): $sin C = \frac{n _{C}}{n _{B}} = \frac{( 2/3 ) n}{( 3/4 ) n} = \frac{8}{9}$
½ mark
The beam does not enter C if $sin r \geq sin C$ : $\frac{4}{3} sin θ \geq \frac{8}{9} \Rightarrow sin θ \geq \frac{2}{3}$ . The beam is then totally reflected at B–C, so it never enters C. Equivalently, $n sin θ = \frac{2}{3} n sin θ_{C}$ would require $sin θ_{C} = \frac{3}{2} sin θ \geq 1$ , which is impossible.
1 mark

Answer: TIR conditions: denser to rarer, and i > critical angle. The beam is totally reflected at B–C when sinθ ≥ 2/3.

Where the marks are

States both conditions for TIR (1 mark)
Applies Snell's law at A–B: sin r = (4/3)sinθ (½ mark)
Critical angle at B–C: sin C = 8/9 (½ mark)
Shows that sinθ ≥ 2/3 gives TIR at B–C (1 mark)

Revise the chapter

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

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 paper2026 board paper, set 55/1/1: every question, by section.

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CBSE Class 12 Physics 2026: question 28

Hints

Step-by-step solution

Revise the chapter

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