Question

A concave mirror produces three times enlarged image of an object placed $10cm$ in front of it. Calculate the focal length of the mirror $\frac{-v}{u}$.

Answer 1

Step 1: Given data

$m$(magnification power) = $+3$

$u$(object distance) = $-10cm$ (taken negatively because it is on the left side )

Step 2: Formulae used

From magnification formula $m$= $\frac{-v}{u}$

From mirror formula $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

Step 3: Solution

On substituting values in the magnification formula:

$$\begin{gathered} v=-\left(3\right)(-10) \\ =\left(30\right)cm \end{gathered}$$

From mirror formula

$$\begin{gathered} \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \\ \frac{1}{30}+\frac{1}{-10}=\frac{1}{f} \\ \frac{-2}{30}=\frac{1}{f} \\ f=-15cm \end{gathered}$$

The focal length of the mirror is $15cm$.