Question

With a concave mirror, an object is placed at a distance $x_1$ from the principal focus, on the principal axis. The image is formed at a distance $x_2$ from the principal focus. The focal length of the mirror is

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

Answer 1

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


From mirror formula,

$f=\frac{uv}{u+v}$
Here, $u=f+x_1$
and $v=f+x_2$

Substituting in the equation,

$f^2=x_1{x}_2$
i.e $f=\sqrt{x_1{x}_2}$
For detailed solution, see next video.