Question

A very thin rod of length $5cm$ is placed along the axis of a concave mirror having radius of curvature $30cm$. If one end of its magnified image touches an end of the rod, then find the length of image of rod.

Answer 1

REF.Image

As image is magnified, the image forms beyond C, thus the

object lies between C and F.

If one end of image touches an end of rod, that end

must lie on C, so Ray diagram :-

Let rod be AB and its image be $A^{\prime }{B}^{\prime }$

A and A' coincide at C.

using Mirror Formula for end B.

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f},u=-25cm$ $f=-15cm$

$\Rightarrow \frac{1}{v}=\frac{1}{-15}-\frac{1}{-25}=\frac{-2}{75}\Rightarrow v=-37.5cm$

so length of image,

$l=7.5cm$ (from diagram)