Question

A candle is placed in front of a concave mirror of focal length 10 cm. A virtual image of the candle is obtained at a distance of 15 cm from the pole of the mirror. The height of the image is 30 cm.

The height of the given candle is

Answer 1

Using the mirror formula
$$\begin{gathered} \frac{1}{f}=\frac{1}{v}+\frac{1}{u} \\ \frac{-1}{10}=\frac{1}{15}+\frac{1}{u} \\ \frac{1}{u}=-\frac{1}{15}-\frac{1}{10} \\ u=-6cm \end{gathered}$$

and since ,

$$\begin{gathered} \frac{H}{h}=\frac{-v}{u}whereHisimageheightandhisobjectheight \\ \frac{30}{h}=-\frac{15}{-6} \\ h=12cm \end{gathered}$$