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

The correct option is B $$\frac{y}{2x}$$

When mirror is rotated by $\theta$ angle reflected ray will be rotated by $2\theta$ (because of law of reflection).

$\frac{y}{x}=\tan 2\theta$
Taking small angle approximation
$\theta =\frac{y}{2x}$