Question

A concave mirror of focal length $20cm$ is cut into two parts from the middle and the two parts are moved perpendicularly by a distance $1cm$ from the previous principal axis $AB$. Find distance between the images formed by the two parts?

Answer 1

Let $P_1{Q}_1=$ principal axis for the mirror $M_1\&P_2{Q}_2=$ principal axis for the mirror $M_2$ ($I_1=$ Image formed by $M_1,I_2=$ Image formed by $M_2$)

Height of object and image are major with respect to principal axis of respective mirror.

Applying convention, we have, $f=-20cm$ (concave), $u=-10cm$

and by Mirror formula $⟹\frac{1}{-10}+\frac{1}{v}=\frac{1}{-20}⟹v=20cm$

$m=\frac{-v}{u}=\frac{-20}{-10}=2=\frac{h_i}{h_o}⟹h_i=2cm$

(+ve magnification means image and object are on th esame side wuth respect to principal axis.)

$h_{I}1=2cm$ below the principal axis $P_1{Q}_1$

$h_{i}2=2cm$ above the principal axis $P_2{Q}_2⟹I_1{I}_2=2cm$