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

Options

A. `(A_(1)+A_(2))/(2)`
B. `[(1)/A_(1)+(1)/A_(2)]^(-1)`
C. `sqrt(A_(1)A_(2))`
D. `[(sqrt(A_(1))+sqrt(A_(2)))/(2)]^(2)`

Answer

C

Explanation

`m_(1)=(A_(1))/(O)` and `m_(2)=(A_(2))/(O)`
`impliesm_(1)m_(2)=(A_(1)A_(2))/(O_(2))`
Also it can be proved that `m_(1)m_(2)=1`
So `O=sqrt(A_(1)A_(2))`