Q. 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 or light is
A) $\frac{A_{1} + A_{2}}{2}$
B) $\left\lbrack \frac{1}{A_{1}} + \frac{1}{A_{2}} \right\rbrack^{- 1}$
C) $\sqrt{A_{1}A_{2}}$
D) $\left\lbrack \frac{\sqrt{A_{1}} + \sqrt{A_{2}}}{2} \right\rbrack^{2}$
Explanation
(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 $O = \sqrt{A_{1}A_{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.