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Find velocity of spot

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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