Question

A candle flame $1.6$ cm high is imaged in a ball bearing of diameter 0.4 cm. If the ball bearing is $20cm$ away from the flame, find the location and the height of the image.

Answer 1

The mirror formula is given as,

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

$\frac{1}{\left(-20\right)}+\frac{1}{v}=\frac{2}{0.2}$

$v=0.1cm$

The magnification is given as,

$\frac{H_i}{H_o}=-\frac{v}{u}$

$\frac{H_i}{1.6}=-\frac{0.1}{-20}$

$H_i=0.008cm$

Thus, the location of the image is $0.1cm$ and the height of the image is $0.008cm$.