28. 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 ?

28. 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 ?

(a) \( \sqrt{A_1 A_2} \)

(b) \( \frac{A_1 + A_2}{2} \)

(c) \( \frac{A_1 - A_2}{2} \)

(d) \( \frac{1}{A_1} + \frac{1}{A_2} \)

Answer :  (a) \( \sqrt{A_1 A_2} \)

\( A_1 = h_1^2 \)

\( A_2 = h_2^2 \)

\( h_0 = \sqrt{h_1 \cdot h_2} \)

\( A_0 = h_0^2 \)

\( \quad = h_1 \cdot h_2 \)

\( \quad = \sqrt{A_1 \cdot A_2} \)