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Shown in the figure are two plane mirrors XY and YZ (XY ⊥ YZ) joined a

June 1, 2025 by rawan239

Shown in the figure are two plane mirrors XY and YZ (XY ⊥ YZ) joined at their edge. Also shown is a light ray falling on one of the mirrors and reflected back parallel to its original path as a result of this arrangement. The two mirrors are now rotated by an angle θ to their new position X’Y’Z’, as shown. As a result the new reflected ray is at an angle α from the original reflected ray. Then :

α = 0

α = θ

α = 2θ

α = 4θ

This question was previously asked in

UPSC NDA-1 – 2023

Download PDF Attempt Online

For a ray of light reflecting successively from two plane mirrors placed perpendicular to each other, the final reflected ray is always anti-parallel to the incident ray, regardless of the initial angle of incidence.

This property is characteristic of a corner reflector made of two perpendicular mirrors. The total deviation after two reflections is 180 degrees. When the mirrors are rotated together by an angle θ, the angle between them remains 90 degrees. Therefore, the property holds true, and the final reflected ray remains anti-parallel to the incident ray.

Since the original reflected ray is anti-parallel to the incident ray and the new reflected ray is also anti-parallel to the *same* incident ray, the two reflected rays are parallel to each other and in the same direction (anti-parallel to the incident ray). The angle between them, α, is 0.

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