Hey!
As we know, when plane mirror rotates through an angle θ , the reflected ray from the mirror rotates through an angle 2θ. So, spot on the screen will make 2 x n = 2n revolutions per second (frequency).
To find the velocity :
v=2πR x frequency
=2π x R x 2n
=4πnR m/s
Hope it helped to clear your delimma.
Thank you.
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