Question

The figure below depicts a concave mirror with center mirror with center of curvature `C` focus `F`, and a horizontally drawn `OFC` as the optic axis. The radius of curvature is `R(OC=R)` and `OF=R//2`). A ray of light `QP`, parallel to the optical axis and at a perpendicular distance `(wleR2)` from it, is incident on the mirror at `P`. It is reflected to the point `B` on the optical axis, such that `BF=k`. Here `k` is a measure of lateral aberrotion

(a) Express `k` in terms of `{w,R}.k="___________________"`
(b) Sketch `k` vs `w` for `w in[0,R//2]`
(c) Consider points `P_(1)P_(2)...........P_(n)` on the concave mirror which are increasingly further away from the optic centre `O` and approximately equidistant from each other (see figure below). Rays parallel to the optic axis are incedent at `P_(1),P_(2).........P_(n)` and reflected to points on the optic axis. Consider the points where these rays reflected from `P_(n),P_(n-1),............P_(2)` intersect the rays reflected from `P_(n-1),P_(n-2),.......P_(1)` respectively. Qualitatively sketch the locus of these points in figure below for a mirror (shown with solid line) with radius of curvature `2 cm`.

Answer 1

Correct Answer - (a) `k=(R)/(2)[(R)/((R^(2)-omega^(2))^(1//2))-1]`
(a) `k =(R)/(2) [(R)/((R^(2)-omega^(2))^(1//2))-1]`
(b)
(c)