Question

A convex of focal length 10.0cm is used to form a real image which is half the size of the object. How far from the object is the image?

Answer 1

$\frac{1}{a}+\frac{1}{b}=\frac{1}{f}$

$\beta=\frac{b}{a}=0.5\to b=0.5a$

$\frac{1}{0.5b}+\frac{1}{b}=\frac{1}{f}\to \frac{3}{b}=\frac{1}{f}\to b=3f=$

$=3\cdot 10.0=30(cm)$