A light ray is incident, at an incident angle θ₁, on the system of tow plane mirrors M₁ and M₂ having an inclination angle 75° between them (as shown in figure). After reflecting from mirror M₁ it gets reflected back by the mirror M₂ with an angle of reflection 30°. The total deviation of the ray will be _____________ degree.

Solution

Physics sir · 4 steps

Find the glancing angle at each mirror from the triangle, then add the two deviations of 180° - 2i.

1. Angle at M2. The angle of reflection at M₂ is 30°, measured from the normal. So the ray makes 90° - 30° = 60° with the surface of M₂.
2. Angle at M1. The ray travelling from M₁ to M₂ forms a triangle with the two mirrors. Its angles are 75° at the vertex and 60° at M₂, so the angle at M₁ is 180° - 75° - 60° = 45°. That gives θ₁ = 90° - 45° = 45°.
3. Deviation at each mirror. A reflection at angle of incidence i turns the ray through 180° - 2i. At M₁ this is 180° - 90° = 90°. At M₂ it is 180° - 60° = 120°. Both turns are in the same sense, so they add.

   δ = (180° - 2× 45°) + (180° - 2× 30°) = 90° + 120°

4. So. The total deviation is 210°, which matches 360° - 2× 75°. The answer is 210.

The common slip: 150. Taking the deviation as 2i at each mirror instead of 180° - 2i gives 90° + 60° = 150, which is the angle on the other side of the ray, not the deviation.

The idea to keep. Each reflection deviates a ray by 180° - 2i. For two plane mirrors at angle θ, the total deviation is always 360° - 2θ, whatever the incidence angle.

Answer from the NTA final answer key. Solution by PrepWiser.