Question

Define the focal length of a spherical mirror. A concave mirror produces $3$ times a real image of an object placed at a distance of $10cm$ in front of it. Find the radius of curvature of the mirror.

Answer 1

Focal length of the spherical mirror is defined as the distance of pole of mirror from the point on the axis of the mirror at which the rays, parallel to the principle axis, appear to converge. In other words, distance between the pole of mirror and the focus point called as the focal length of mirror.

Given : Magnification ,$m=-3$ Object distance, $u=-10cm$

Using $m=\frac{-v}{u}$

$\therefore$ $-3=\frac{-v}{-10}$

$⟹v=-30cm$

Now using, $\frac{1}{v}+\frac{1}{u}=\frac{2}{R}$

$\therefore$ $\frac{1}{-30}+\frac{1}{-10}=\frac{2}{R}$

$⟹R=-15cm$