A plane mirror is approaching you at a speed | vedclass

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Question

(C) Let the distance between the object (you) and the plane mirror be $x$ at any instant.Since the image formed by a plane mirror is at the same dista

Vedclass · Accepted Answer

$20$

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(C) Let the distance between the object (you) and the plane mirror be $x$ at any instant.Since the image formed by a plane mirror is at the same distance behind the mirror as the object is in front of it, the distance of the image from the mirror is also $x$.When the mirror moves towards the object by a distance $y$, the new distance between the object and the mirror becomes $(x - y)$.The new position of the image will be at a distance $(x - y)$ behind the mirror.The initial distance of the image from the object was $2x$.The final distance of the image from the object is $(x - y) + (x - y) = 2(x - y) = 2x - 2y$.The change in the distance of the image from the object is $2x - (2x - 2y) = 2y$.Since the change in distance is $2y$ for a displacement $y$ of the mirror, the speed of the image relative to the object is twice the speed of the mirror.Speed of image $= 2 	imes 	ext{speed of mirror} = 2 	imes 10\,cm/sec = 20\,cm/sec$.

$A$ plane mirror is approaching you at a speed of $10\,cm/sec$. You can see your image in it. At what speed will your image approach you in $cm/sec$?

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