Question

a stick of length f/2 is placed on principal axis of a concave mirror of focal length f such that the image of one end coincides. then the length of its image will be

Answer 1

look at the attachment

• Length of rod given by f/2

Radius of the culvature=2f

Now

• Object distance =PC-AB=2f-f/2=4f-f/2=-3f/2

Applying Mirror formula

$\\ \rm\longmapsto \dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$

$\\ \rm\longmapsto \dfrac{1}{v}=\dfrac{1}{u}+\dfrac{1}{f}$

$\\ \rm\longmapsto \dfrac{1}{v}=\dfrac{1}{-3f/2}+\dfrac{-1}{f}$

$\\ \rm\longmapsto \dfrac{1}{v}=-\dfrac{2}{3f}-\dfrac{1}{f}$

$\\ \rm\longmapsto \dfrac{1}{v}=\dfrac{2-3}{3f}$

$\\ \rm\longmapsto \dfrac{1}{v}=\dfrac{-1}{3f}$

$\\ \rm\longmapsto v=-3f$

• v is iage distance

Now

$\\ \rm\longmapsto m=\dfrac{h'}{h}=-\dfrac{v}{u}=$

$\\ \rm\longmapsto m=\dfrac{f}{f/2}$

$\\ \rm\longmapsto m=2$