A lens if 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

Options

A. `(A_1+A_2)/(2)`
B. `[(1)/(A_1)+(1)/(A_2)]^-1`
C. `sqrt(A_1A_2)`
D. `[(sqrtA_1+sqrt_2)/(2)]^2`

Answer

C

Explanation

`(A_1)/(A_O)=m_1^2impliesm_1=sqrt((A_1)/(A_O))=(I_1)/(O)`
`(A_2)/(A_O)=m_2^2impliesm_2=sqrt((A_2)/(A_O))=(I_2)/(O)`
`m_1m_2=(I_1I_2)/(O^2)=sqrt((A_1)/(A_O))xxsqrt((A_2)/(A_O))=1`
`A_O=sqrt(A_1A_2)`