A ray of light is incident on a plane. The mirror is then turned through an angle α keeping the direction of the incident ray constant. If the reflected ray turned through an angle β, find the relationship between α and β. Or Derive the relation between the angle of rotation of a plane mirror and the angle of deflection of a reflected ray, when the direction of the incident ray is constant.

A ray of light is incident on a plane. The mirror is then turned through an angle α keeping the direction of the incident ray constant. If the reflected ray turned through an angle β, find the relationship between α and β.

Or

Derive the relation between the angle of rotation of a plane mirror and the angle of deflection of a reflected ray, when the direction of the incident ray is constant.

Solution

Let XY be the initial position of the mirror with ray AO making a glancing angle g. By keeping the direction of the incident ray fixed, the mirror is rotated through an angle α to a new position X’Y’ as shown.

Case 1 (mirror in position XY)

Glancing angle = g

Deviation d1 = 2g……… (i)

Case 2(mirror in position X’Y’)

Glancing angle = (g – α)

Deviation d₂ = 2(g – α) …..(ii)

θ = d₁ –d₂

= 2g – 2(g – α)

= 2g-2g + 2α

= 2α

Thank u

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