• # question_answer 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 (source and wall are fixed)- A) ${{({{A}_{1}}{{A}_{2}})}^{1/2}}$ B) $\frac{{{A}_{1}}+{{A}_{2}}}{2}$ C) ${{\left( \frac{1}{{{A}_{1}}}+\frac{1}{{{A}_{2}}} \right)}^{-1}}$      D) ${{\left( \frac{\sqrt{{{A}_{1}}}+\sqrt{{{A}_{2}}}}{2} \right)}^{2}}$

 From Nerwton's equation of lens size of object  = ${{O}^{2}}={{l}_{1}}{{l}_{2}}$ where ${{l}_{1}}$ is size of image of object and ${{l}_{2}}$is size of image when positions of object & image are interchanged So ${{A}^{2}}={{A}_{1}}{{A}_{2}}\Rightarrow \mathbf{A}=\sqrt{{{A}_{1}}{{A}_{2}}}$