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Question

A short linear object of length L lies on the axis of a spherical mirror of focal length f at a distance b from the mirror. Find the size of the image.

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Solution

1v+1u=1f
By differentiating both sides
dvv2=duu2
du: size of object =L; dv:size of image;
u: object distance
v: image distance
dv=v2u2du (1v=1f1uv=fuuf)
=f2u2(uf)2u2du=f2(bf)2L
Negative sing implies that object is lying between u and u+ and the image will lie between v and vdv

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