Question

A lens is placed between a source of light and a wall. It forms images of area $A_{1}$ and $A_{2}$ on the wall for its two different positions. The area of the source of light is

• A. $\frac{A_{1}+A_{2}}{2}$
• B. $\left[\frac{1}{A_{1}}+\frac{1}{A_{2}}\right]^{-1}$
• C. $\sqrt{A_{1} A_{2}}$
• D. $\left[\frac{\sqrt{A_{1}}+\sqrt{A_{2}}}{2}\right]^{2}$

Answer 1

Answer: (C)

$m_{1}=\frac{A_{1}}{O}$ and $m_{2}=\frac{A_{2}}{O}$
$\Rightarrow m_{1} m_{2}=\frac{A_{1} A_{2}}{O_{2}}$
Also it can be proved that $m_{1} m_{2}=1$
So $O=\sqrt{A_{1} A_{2}}$