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_________ $\mathrm{cm}$.
Solution:
$m=\frac{f}{u+f}$
$+m=\frac{f}{-10+f}$..........(1)
$-m=\frac{f}{-20+f} \quad \cdots$(2)
(1) / (2)
$-1=\frac{f-20}{f-10}$
$10-f=f-20$
$30=2 f$
$f=15 \mathrm{~cm}$