Question

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:

• A. $\frac{x}{y}$
• B. $\frac{y}{2x}$
• C. $\frac{y}{x}$
• D. $\frac{x}{2y}$

Answer 1

Answer: (B)

$\frac{y}{2x}$

If mirror is rotated by angle $\theta$
angle of refrection is $2\theta$
$\tan 2\theta =\frac{y}{x}$
$2\theta =y/x$
$\theta =y/2x$