Question

When an object is $40$cm away from pole of a concave spherical mirror, the size of the image is equal to that of object.
The focal length of the mirror is__________

Answer 1

Step $1$: Given data

Given: $u$ is the object distance from pole and $v$ is the image distance
$u=-40cm$
$m$ is magnification
$m=-1$
Step $2$: Finding the value of $v$

We have a magnification formula,

$$\begin{gathered} m=\frac{-v}{u} \\ -1=-\frac{v}{u} \\ v=u \\ =-40cm \end{gathered}$$

Step $3$: Finding the value of focal length

We have a formula,$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$

$\frac{-1}{40}-\frac{1}{40}=\frac{1}{f}$

$\frac{-2}{40}=\frac{1}{f}$

$f=-20cm$
Thus, the focal length of the mirror is $20cm$.