Question:
The same size images are formed by a convex lens when the object is placed at $20 \mathrm{~cm}$ or at $10 \mathrm{~cm}$ from the lens. The focal length of convex lens is______ cm.
Solution:
(15)
$\frac{1}{v}-\frac{1}{v}=\frac{1}{f} \ldots(1)$
$m=\frac{v}{w} \ldots(2)$
from (1) and (2) we get $m=\frac{f}{f+u}$
given conditions
$m_{1}=-m_{2}$
$\frac{f}{f-10}=\frac{-f}{f-20}$
$f-20=-f+10$
$2 f=30$
$\mathrm{f}=15 \mathrm{~cm}$
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