JEE Advanced 2022 Paper 1 Q12 Physics Waves & Optics Reflection of Light Hard

JEE Advanced 2022 Paper 1 · Q12 · Reflection of Light

Three plane mirrors form an equilateral triangle with each side of length L. There is a small hole at a distance l > 0 from one of the corners as shown in the figure. A ray of light is passed through the hole at an angle θ and can only come out through the same hole. The cross section of the mirror configuration and the ray of light lie on the same plane. Which of the following statement(s) is(are) correct?

[Figure: Equilateral triangle formed by three plane mirrors of side L, with a small hole at distance l from one corner on one of the sides; a ray entering at angle θ to that side.]

  1. A. The ray of light will come out for θ = 30°, for 0 < l < L.
  2. B. There is an angle for l = L/2 at which the ray of light will come out after two reflections.
  3. C. The ray of light will NEVER come out for θ = 60°, and l = L/3.
  4. D. The ray of light will come out for θ = 60°, and 0 < l < L/2 after six reflections.
JEE Advanced multi-correct — pick every correct option, then check.
Reveal answer + step-by-step solution

Correct answer:A, B

Solution

For an equilateral-triangle mirror cavity (image method), the only entry angles for which a ray that enters through a single hole can return to that same hole are those that produce a closed geometric path. (A) θ = 30°: the ray hits the next mirror perpendicularly, retraces itself, and exits through the same hole regardless of l ∈ (0, L); correct. (B) For l = L/2 (midpoint), there exists an angle θ for which after two reflections the ray comes back through the hole (using the perpendicular-bisector symmetry); correct. (C) For θ = 60° and l = L/3, a closed three-bounce path exists (it traces the inner medial triangle), so the ray does come out; the statement that it NEVER comes out is wrong. (D) For θ = 60° with arbitrary l ∈ (0, L/2), a six-reflection return is not generally guaranteed; incorrect. Hence (A) and (B) are correct.

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