Question

In a concave mirror experiment, an object is placed at a distance $x_1$ from the focus and a real 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. $\frac{x_1}{x_2}$

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 can be calculated as
$f=\frac{uv}{u+v}$
Substituting $u$ and $v$, we get
$f^2=x_1{x}_2\Rightarrow f=\sqrt{x_1{x}_2}$