Question

A candle flame $1cm$ high is imaged in a ball bearing of diameter $0.4cm$ . If the ball bearing is $20cm$ away from the flame, find the location and the height of the image.

Answer 1

We know that

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

By substituting the values in the above given equation we get

$\frac{1}{-20}+\frac{1}{v}=\frac{2}{0.2}$

We get the $v=0.1cm$inside the ball bearing

The magnification$m=\frac{-v}{u}$

$m=\frac{1}{200}$

Also the magnification can be given as

$m=\frac{h_i}{h_f}$

Equating the above equation we get the height of the image

$h_i=\frac{16}{200}=0.8mm$