A beam of light from a source `L` is incident normally on a plane mirrorr fixed at a certain distance `x` from the source. The beam is reflected back as a spot on a scale placed just above the source `L`. When the mirrorr is rotated through a small angle `theta`, the spot of the light is found to move through a distance `y` on the scale. The angle `theta` is given by `:`

Options

A. `(y)/(x)`
B. `(x)/(2y)`
C. `(x)/(y)`
D. `(y)/(2x)`

Answer

D

Explanation

When mirror is rotated by `theta` angle reflected ray will be rotated by `2theta`.
For small angle `theta,tan2theta~~2theta=(y)/(x)`
`:. theta =(y)/(2x)`