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For a fixed incident light ray, if the m...

For a fixed incident light ray, if the mirror be rotated through and angle `theta` (about an axis which lies in the plane of mirror and perpendicular to the plane of incidence), show that the reflected ray turns through an angle 2`theta` in same sense.

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In Fig. , `M_1,N_1`,and `R_1` indicate the initial position of mirror, normal, and direction of reflected light ray, respectively, `M_2,N_2`, and `R_2` indicate the final position of mirror, normal, and direction of reflected light ray, respectively.
If the mirror is rotated by and angle `theta,` new angle of incidence
`=angleABN_2=phi+theta`
Angle of deviation of final ray `=angleDBC=delta`
`angleDBC = angleABC-angleABD=2(phi+theta)-2phi=2theta`
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