# Two objects P and Q when placed at different positions in front of a concave mirror of focal length 20 cm, form real images of equal size. Size of object P is three times size of object Q. If the distance of P is 50 cm from the mirror, find the distance of Q from the mirror.

For P

$m=\frac{h_2}{h_1}=\frac{f}{f-u_1}$

$m'=\frac{h_2'}{h_1'}=\frac{f}{f-u_2}$

$\\\frac{m}{m'}=\frac{h_2h_1'}{h_1h_2'}=\frac{f-u_2}{f-u_1}=\frac{-20-u_2}{-20+50}\\10=-20-u_2\\implies\\u_2=-30cm$

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