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Consider a convex lens with $f$ focal length in $f$ distance from a wall. Principle axis is perpendicular to the wall. A mirror is rotating with $\omega$ angular velocity so that axis of rotation is perpendicular to principle axis .

Parallel rays of light incident on the mirror. After reflecting the light ray and passing the lens , a spot is created on the wall. In this diagram , rays after reflection from the mirror is parallel to principle axis of the lens and the created spot on the wall in point $F$ is focal point. What is the velocity of spot exactly in this time ?

My try :It's too complicated problem for me and really I don't have any idea.

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  • $\begingroup$ Did you need further help or clarification than my answer currently provides? $\endgroup$
    – bpedit
    Commented Feb 12, 2017 at 15:25
  • $\begingroup$ @bpedit Can you say the final answer for making sure ? $\endgroup$
    – S.H.W
    Commented Feb 12, 2017 at 16:37

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You must mean the angular velocity of the spot since there is no indication of the distance to the wall for the answer to be in linear terms. So let's plan to give the answer in terms of the angular velocity of the mirror.

Draw a ray diagram showing the path of a ray when the mirror is at 45° to the principal axis. What is the angle between the incident and the reflected ray?

Now draw a diagram where the mirror is at 90°, or parallel, to the principal axis.

So, how much has the reflected ray rotated compared to how much the mirror has rotated?

Also think about it like this. As you rotate the mirror, the normal, where a ray strikes, rotates along with the mirror at the same angular velocity. But the ray itself makes two angles relative to that normal, the incident ray and the reflected ray. So every change in the mirrors angle changes both these angles.

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  • $\begingroup$ Can you say the final answer for making sure ? $\endgroup$
    – S.H.W
    Commented Feb 12, 2017 at 16:35
  • $\begingroup$ The beam is rotating twice as fast as the mirror. $\endgroup$
    – bpedit
    Commented Feb 12, 2017 at 17:04

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