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JEE Advanced 2025 · Paper 2, Physics question 6

Two identical concave mirrors each of focal length ff are facing each other as shown in the schematic diagram. The focal length ff is much larger than the size of the mirrors. A glass slab of thickness tt and refractive index n0n_0 is kept equidistant from the mirrors and perpendicular to their common principal axis. A monochromatic point light source SS is embedded at the center of the slab on the principal axis, as shown in the schematic diagram. For the image to be formed on SS itself, which of the following distances between the two mirrors is/are correct:

Two identical concave mirrors (focal length f) face each other on a common horizontal principal axis (dashed). Midway between them a vertical glass slab of thickness t and refractive index n₀ stands perpendicular to the axis, with the point source S (star) at its centre on the axis.
Choose one or more options
Answer and worked solution

Official answer: A, B

Apparent shift. Seen through the slab, S appears displaced towards each mirror by t2(1−1n0)\frac t2\left(1-\frac1{n_0}\right). Equivalently, the slab adds t(1−1n0)t\left(1-\frac1{n_0}\right) to the required separation.

Two ways the image returns to S.

  • S at each mirror's centre of curvature. Light returns along its own path. The separation is 2⋅2f+(1−1n0)t2\cdot2f+\left(1-\frac1{n_0}\right)t. (A)
  • S at each mirror's focus. Light from S becomes parallel after one mirror, then the other mirror focuses it back on S. The separation is 2f+(1−1n0)t2f+\left(1-\frac1{n_0}\right)t. (B)
Topics:Spherical mirrorsRefraction at plane surfaces
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