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Difficulty: MediumReflection of Light at Plane and Curved Mirrors

A light ray strikes a plane mirror. Keeping the direction of the incident ray fixed, the mirror is rotated through an angle of 15∘15^\circ about an axis lying in its plane. What is the angle of rotation, in degrees, of the reflected ray?

Answer: 30 degrees

Answer

The reflected ray turns through an angle of 30∘30^\circ.
When a plane mirror is rotated through an angle θ\theta while keeping the incident ray direction constant, the normal turns by θ\theta. This changes the angle of incidence by θ\theta and the angle of reflection by θ\theta, causing the reflected ray to rotate by a total angle of 2θ2\theta. For a mirror rotation of 15∘15^\circ, the reflected ray rotates through 2×15∘=30∘2 \times 15^\circ = 30^\circ.

Step-by-Step Solution

1
Analyze the effect of mirror rotation on the normal line
When the plane mirror rotates by 15∘15^\circ, the normal to the mirror surface also rotates by 15∘15^\circ.
The normal line is always perpendicular to the surface of the mirror.
2
Determine the change in the angle of incidence and reflection
The angle of incidence changes by 15∘15^\circ, so the angle of reflection relative to the new normal also changes by 15∘15^\circ.
According to the law of reflection, the angle of incidence equals the angle of reflection (i=ri = r).
3
Calculate the total angular deviation of the reflected ray
The total shift of the reflected ray relative to its original path is 15∘+15∘=30∘15^\circ + 15^\circ = 30^\circ.
The rotation of the reflected ray is twice the angle of rotation of the mirror.

Key Concept

Rotation of Reflected Ray by a Plane Mirror
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Topics

Reflection of Light at Plane and Curved Mirrors

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