A lens is placed between a source of light and a wall. It forms images of area A1 and A2 on the wall for its two different positions. The area of the source of light is

Question

A lens is placed between a source of light and a wall. It forms images of area A1 and A2 on the wall for its two different positions. The area of the source of light is (A) (A1+A2/2) (B) [(1/A1)+(1/A2)]-1 (C) √A1 A2 (D) [(√A1+√A2/2)]2

Tardigrade Admin · Accepted Answer

m1=(A1/O) and m2=(A2/O) ⇒ m1 m2=(A1 A2/O2) Also it can be proved that m1 m2=1 So O=√A1 A2

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 of light is

$\frac{A _{1} + A _{2}}{2}$

$[\frac{1}{A _{1}} + \frac{1}{A _{2}}]^{- 1}$

$A_{1} A_{2}$

$[\frac{A _{1} + A _{2}}{2}]^{2}$

$m_{1} = \frac{A _{1}}{O}$ 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 $O = A_{1} A_{2}$

Q. A lens is placed between a source of light and a wall. It forms images of area A1​ and A2​ on the wall for its two different positions. The area of the source of light is

2A1​+A2​​

[A1​1​+A2​1​]−1

A1​A2​​

[2A1​​+A2​​​]2