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

Answer 1

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

Applying mirror formula:
$1/v+1/u=1/f$


$u=-(x_1+f)v=-(x_2+f)-\frac{1}{x_2+f}-\frac{1}{x_1+f}=\frac{-1}{f}$
$\frac{x_1+f+x_2+f}{(x_1+f)(x_2+f)}=\frac{1}{f}f(2f+x_1+x_2)=(x_1+f)(x_2+f)2f^2+f{x}_1+f{x}_2=x_1{x}_2+f{x}_1+f{x}_2+f^2$
$\begin{array}{c}f=\sqrt{x_1{x}_2}\end{array}$