A beam of light from a source L is incident normally on a plane mirror 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 mirror 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

B, D

Explanation

When plane mirror is given rotation of `theta`, then reflected ray will have rotation `2theta`. In figure,
In right angle triangle tan`2theta=y/x`
For smaller angle, `tan2theta ~~2 theta`
`therefore 2 theta=y/x therefore theta=(y)/(2x)`