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

1. y / x
2. x / 2y
3. x / y
4. y / 2x

Correct answer: y / 2x

Solution

When the mirror is rotated by an angle θ, the reflected beam rotates by 2θ. Using the geometry of the situation, the displacement y on the scale is related to the angle of rotation by the formula θ = y / 2x, where x is the distance between the mirror and the scale.

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