A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance 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 , the spo

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Solution

Q.
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 [2017]

1 $\frac{y}{x}$

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

3 $\frac{x}{y}$

4 $\frac{y}{2 x}$

Ans.
(4)

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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