Reflected beam is rotated through an angle of 2x
We see that on rotating the mirror by angle x, the angle of incidence changes from i to i + x
Initially , angle between incident ray and reflected ray = i1 + r1 = i1 + i1 = 2i1
After rotation of mirror:-
Angle between same incident ray and rotated reflected ray = i2 + r2 = i2 + i2 = 2i2
( since i = r )
2i2 = 2(i1 + x) = 2i1 + x
Hence, reflected ray is rotated by angle
(2i1 + 2x - 2i1 ) = 2x
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