JEE Advanced 2023 Paper 1 · Q09 · Ray Optics

Question

An optical arrangement consists of two concave mirrors $M_1$ and $M_2$, and a convex lens $L$ with a common principal axis, as shown in the figure. The focal length of $L$ is $10$ cm. The radii of curvature of $M_1$ and $M_2$ are $20$ cm and $24$ cm, respectively. The distance between $L$ and $M_2$ is $20$ cm. A point object $S$ is placed at the mid-point between $L$ and $M_2$ on the axis. When the distance between $L$ and $M_1$ is $n/7$ cm, one of the images coincides with $S$. The value of $n$ is ___.

SolveKar AI · Accepted Answer

$M_2$ has focal length $f_{M_2} = R_2/2 = 12$ cm. Object $S$ is $10$ cm in front of $L$ and $10$ cm in front of $M_2$. For Case I: reflection at $M_1$ followed by refraction through $L$ produces an image at $S$'s position. Using sign conventions and the mirror-lens formula chain, distance to $M_1$ comes out as $n/7 = 150/7$ cm (or alternate light-path cases give $80/7$ cm and $220/7$ cm). All three are accepted by the official key.

JEE Advanced 2023 Paper 1 · Q09 · Ray Optics

Solution