Question

Figure shown a spherical concave mirror with its pole at (0,0) and principal axis along x axis. There is a point object at (-40 cm, 1cm), find the position of image.

Answer 1

$f=\frac{R}{2}=10cm$

and the focal length of concave mirror is $-ve$, Hence $f=-10cm$

$u=-40cm$ and $h_o=1cm$

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$⟹\frac{1}{v}=\frac{1}{f}-\frac{1}{u}=\frac{-1}{10}+\frac{1}{40}$

$⟹v=\frac{-40}{3}cm$

Magnification $m=\frac{-v}{u}=\frac{h_i}{h_o}$

$⟹h_i=-\frac{-40}{-40\times 3}\times 1$

$⟹h_i=-\frac{1}{3}$

Hence , position of image is-

$(\frac{-40}{3},\frac{-1}{3})$