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Two mirrors AB and CD are placed as shown with their reflecting surfaces towards each other. A ray of light incident on AB at $$45^\circ$$ on reflection from AB and CD emerges parallel to the original direction. Through what angle (in degrees) does the ray reflected by CD turn if<br>i) AB is turned in a clock wise sense through a small angle $$5^\circ$$.<br>ii) CD is turned in anticlockwise sense through a small angle $$5^\circ$$.
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Correct Answer: 10
Turning a mirror through an angle $$\theta$$ turns the reflected ray through $$2\theta$$. i) Turning AB by $$5^\circ$$ turns the ray going to CD by $$10^\circ$$, and the reflection at the fixed mirror CD turns the final ray by the same $$10^\circ$$. ii) Turning CD by $$5^\circ$$ directly turns the ray it reflects by $$2 \times 5^\circ = 10^\circ$$. In both cases the ray reflected by CD turns through $$10^\circ$$.
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