JEE Advanced 2025 Paper 2 Q06 Physics Waves & Optics Ray Optics – Mirrors Hard

JEE Advanced 2025 Paper 2 · Q06 · Ray Optics – Mirrors

Two identical concave mirrors each of focal length $f$ are facing each other. The focal length $f$ is much larger than the size of the mirrors. A glass slab of thickness $t$ and refractive index $n_0$ is kept equidistant from the mirrors and perpendicular to their common principal axis. A monochromatic point light source $S$ is embedded at the center of the slab on the principal axis. For the image to be formed on $S$ itself, which of the following distances between the two mirrors is/are correct:

  1. A. $4f + (1 - 1/n_0)\,t$
  2. B. $2f + (1 - 1/n_0)\,t$
  3. C. $4f + (n_0 - 1)\,t$
  4. D. $2f + (n_0 - 1)\,t$
JEE Advanced multi-correct — pick every correct option, then check.
Reveal answer + step-by-step solution

Correct answer:A, B

Solution

Apparent shift of the source as seen by either mirror due to the half-slab in front of it equals $(1 - 1/n_0)(t/2)$ on each side; the total apparent shortening of the air-path between the source and a mirror across the full slab is $(1 - 1/n_0)\,t$ (since light traverses the slab on going and on returning, but the shift counts once for object and once for image). Self-imaging case 1 (object at center of curvature $2f$ for each mirror): the geometric distance between mirrors must satisfy $d - (1 - 1/n_0)\,t = 4f$, i.e., $d = 4f + (1 - 1/n_0)\,t$. (A) TRUE. Self-imaging case 2 (light from $S$ returns parallel after first mirror, then converges back to $S$ after the second mirror reflection, requires effective object-mirror distance $= f$): $d = 2f + (1 - 1/n_0)\,t$. (B) TRUE. Options (C) and (D) use the wrong direction of shift ($n_0 - 1$ instead of $1 - 1/n_0$). Correct: (A), (B).

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