A small plane mirror is placed at the centre of a spherical screen of radius R. A beam of light is falling on the mirror. If the mirror makes n revolutions per second, the speed of the spot of light on the screen after reflection from the mirror will be

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$\frac{n R}{2 π}$

$\frac{n R}{4 π}$

$2 πnR$

$4 πnR$

answer is D.

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Detailed Solution

If the mirror rotates through an angle $θ$ , the reflected ray rotates through an angle 2 $θ$ . Therefore, the spot on the screen will make 2 n revolutions per second. Hence the speed of the spot will be

$ν = ω R = 2 π \times 2 n \times R = 4 πnR$

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