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Question Visualization
M is mirror, S is point source of light, W is wall where patch will be formed, V is velocity of mirror

See this image when the mirror moves towards wall, a patch will be formed by the rays reflected from the mirror, intuition says it will get bigger as mirror approaches the wall but in reality it doesn't.
Any unique reflected ray is moving towards source(using ray diagram) as mirror moves up. So how is it that a single reflected ray is moving but collectively the patch formed by all the rays is at rest.

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2 Answers 2

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Consider the position of the image of the source as the mirror moves towards the wall.
The rays of light reflected from a plane mirror all appear to come from a virtual image behind the mirror.

enter image description here

The left of the mirror is at $E_1,\,E_2,\, E_3$ and $E_4$ with corresponding image positions $I_1,\,I_2,\, I_3$and $I_4$.

Looking at the geometry of the situation shows that the left-hand side of the illuminated region, $L$, does not move and the same is true of the right-hand side.

enter image description here

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It is correct that the patch formed collectively by all the rays incident on mirror will be at rest. Outline of the patch can be made by ray diagram of the rays incident on two extremes of the mirror, do this for different positions of mirror, it will same for all.

For second part do an exercise, draw some light rays from source S to the mirror M, make sure that two of them are at the extremities of the mirror. Now move the mirror towards the wall, will find that the rays at left extreme of the mirror lose contact with the mirror(do not incident), the rays at the right extreme stats to come in contact(incident).

Therefore, it is correct that all reflected points move with -$V \sin\theta$, where $\theta$ is angle formed by that ray with normal to the mirror and negative signifies that the reflected point moves towards S, but when the ray loses the contact there is no reflection.
Think of patch as a Baggage Carousel looked from a side, and patch formed by a single ray as a ball(baggage). Now even tough Balls are moving but effective length($\sum$Diameter) is constant.

Baggage Carousel analogy gif

See here black line is patch and red dots are single reflected ray patches.

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