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

Answer

A

Explanation

When plane mirror is in position `M`, Fig. the beam of light from source at a distance `x` from the source is formed just above `L`. When mirror is rotated through a small angle `theta`, the reflected ray (for the same incident ray) turns through an angle `2 theta` and spot of image is formed at `L`, where `LL' = y`.
From Fig.

`tan 2 theta = 2 theta = (y)/(x)`
`theta = (y)/(2 x)`