A ray of light is incident on a plane mirror at an angle of 40° with r

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A ray of light is incident on a plane mirror at an angle of 40° with respect to normal. When it gets reflected from the mirror, it undergoes a deviation of

40°
100°
90°
80°
This question was previously asked in
UPSC CDS-2 – 2017
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When a ray of light is incident on a plane mirror at an angle of 40° with respect to normal, it undergoes a deviation of 80°.
According to the law of reflection, the angle of incidence (i) is equal to the angle of reflection (r), and both are measured with respect to the normal to the mirror surface. Given i = 40°, then r = 40°. Deviation is the angle between the direction of the incident ray and the direction of the reflected ray. If the incident ray were not reflected, it would continue in a straight line. The reflection changes its direction.
The angle between the incident ray and the normal is 40°. The angle between the reflected ray and the normal is 40° on the opposite side of the normal. The total angle between the incident ray and the reflected ray is the sum of the angle between the incident ray and the normal and the angle between the normal and the reflected ray in the plane of reflection, which is 40° + 40° = 80°. This angle represents the deviation of the ray from its original path. Alternatively, the angle between the incident ray and the mirror surface is θ = 90° – i = 90° – 40° = 50°. The angle of deviation (δ) for reflection from a plane mirror is also given by δ = 180° – 2θ = 180° – 2(50°) = 180° – 100° = 80°.

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