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 and 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)`.
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