First slide

The lens

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 or light is

Moderate

A

$\frac{A_{1} + A_{2}}{2}$
B

${[\frac{1}{A_{1}} + \frac{1}{A_{2}}]}^{- 1}$
C

$\sqrt{A_{1} A_{2}}$
D

${[\frac{\sqrt{A_{1}} + \sqrt{A_{2}}}{2}]}^{2}$

Solution

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

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