STEMS 2021 Phy Cat B Q1
Source:
January 23, 2021
Problem Statement
[*]There are two semi-infinite plane mirrors inclined physically at a non-zero angle with the inner surfaces being reflective.\\
Prove that all lines of incident/reflected rays are tangential to a particular circle for any given incident ray being incident on a reflective side. Assume that the incident ray lies on one of the normal planes to the mirrors.[/*]
[*] There's a cone of an arbitrary base with large enough length.\\
The inner surface polished (Outer surface is absorbing in nature) and the apex is fixed to a point. The cone is being rotated around the apex at an angular speed around the vertical axis and assume that a large part of the inside is visible horizontally. A fixed horizontal ray is projected from outside towards the cone (which often falls inside of it), prove that all the lines of incident ray/reflected rays at all instants lie tangential to a particular sphere.\\
Try guessing the radius of the sphere with the parameters you observe.[/*]