A small angled prism of apex angle A = 4° and refractive index μ = 1.5 is placed in front of a vertical plane mirror as shown in figure. If the mirror is rotated through an angle $θ$ , then the light ray becomes horizontal either after the mirror or after second time refraction through the prism. The value of $θ$ is

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1°

Not possible

2°

4°

answer is A, B.

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Detailed Solution

Deviation, $δ = (μ - 1) A = (1.5 - 1) 4 ° = 2 °$

(a)

To rotate ray MP by 2° (to make it parallel to MN) we will have to rotate the mirror only by 1°
(b) Without prism, ray of light was falling normal to plane mirror. So, ray of light was retracing its path prism has deviated it 2°. So if we rotate the mirror by 2°, ray of light further falls normal to plan mirror and retraces its path.

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