Question

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

Answer 1

Height of the object AB = 1.6 cm

Diameter of the ball bearing = d = 0.4 cm

$\Rightarrow R=0.2\text{cm}$

Given, u = 20 cm

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

Putting the values according to sign conventions.

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

$\Rightarrow \frac{1}{v}=\frac{1}{20}+10$

$\Rightarrow v=1\text{cm}$ inside the ball bearing.

Magnification = m

$=\frac{A^{{}^{\prime }}{B}^{{}^{\prime }}}{AB}=\frac{v}{u}$

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

$\Rightarrow A^{{}^{\prime }}{B}^{{}^{\prime }}=\frac{AB}{200}=+\frac{1.6}{200}$

$=+0.008\text{cm}$