First slide

Ray optics

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 $θ$ the spot of the light is found to move through a distance y on the scale. The angle $θ$ is given by

Moderate

A

$\frac{y}{x}$
B

$\frac{x}{2 y}$
C

$\frac{x}{y}$
D

$\frac{y}{2 x}$

Solution

When mirror is rotated by $θ$ angle reflected ray will be rotated by 2 $θ$ .
For small angle $θ$

$\tan 2 θ \approx 2 θ = \frac{y}{x}$
$∴ θ = \frac{y}{2 x}$

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