Question

In a concave mirror experiment, an object is placed at a distance $x_1$ from the focus and the image is formed at a distance $x_2$ from the focus. The focal length of the mirror would be

• A. $x_1{x}_2$
• B. $\sqrt{x_1{x}_2}$
• C. $\frac{x_1{x}_2}{2}$
• D. $\sqrt{\frac{x_1}{x_2}}$

Answer 1

The correct option is B $\sqrt{x_1{x}_2}$

Given $u=(f+x_1)$ and $v=(f+x_2)$
The focal length $f=\frac{uv}{u+v}=\frac{(f+x_1)(f+x_2)}{(f+x_1)+(f+x_2)}$
On solving, we get $f^2=x_1{x}_2$ or $f=\sqrt{x_1{x}_2}$