If a plane mirror is rotated by an angle Q, by how much will the angle between the incident and reflected ray change?

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Detailed Solution

If a plane mirror is rotated by an angle Q, 2Q will be the angle change between the incident and reflected ray.
On rotating the mirror by angle Q, the angle of incidence changes from

i

i + Q

. Initially, the angle between the incident ray and reflected ray =

i_{1} + r_{1} = i_{1} + i_{1} = 2 i_{1}

After rotation of mirror:- Angle between the same incident ray and rotated reflected ray

= i_{2} + {r ​}_{2} = i_{2} + i_{2} = 2 i_{2} ​

(since

i = r

) therefore,

2 i_{2} = 2 (i_{1} + Q) = 2 i_{1} + 2 Q

Hence, reflected ray is rotated by angle

= (2 i_{1} + 2 Q - 2 i_{1}) = 2 Q

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