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Two plane mirrors are inclined at 70°. A ray incident on one mirror at angle θ after reflection falls on second mirror and is reflected from there parallel to first mirror. The value of θ is

1. 50°
2. 30°
3. 45°
4. 55°

Correct answer: 30°

Solution

The total deviation of the ray after two reflections is 2θ + 2(90° - θ) = 180° - 2θ. For the ray to emerge parallel to the first mirror, the total deviation must equal the angle between the mirrors, which is 70°. Solving 180° - 2θ = 70° gives θ = 30°.

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