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

Given,
Height (h₁) of the candle flame taken as object AB = 1.6 cm
Diameter of the ball bearing (d) = 0.4 cm
So, radius = 0.2 cm
Distance of object, u = 20 cm

Using mirror formula,
\[\frac{1}{v} + \frac{1}{u} = \frac{2}{R}\]
Putting the values according to sign conventions, we get,

\[\frac{1}{( - 20)} + \frac{1}{v} = \frac{2}{0 . 2}\] 

\[ \Rightarrow   \frac{1}{v} = \frac{1}{20} + 10\] 

\[ \Rightarrow   v = 0 . 1  cm  or  1 . 0  \text{ mm  inside  the  ball  bearing . }\] 

\[Magnification = m\] 

\[ = \frac{A'B'}{AB} =  - \frac{v}{u} = m\] 

\[ = \frac{A'B'}{200} = \frac{1}{200}\] 

\[\Rightarrow A'B'=\frac{AB}{200}=+\frac{1 . 6}{200} =  + 0 . 08  \text{ cm }  (+0008\text{ cm })\]

Hence, the distance of the image is 1 cm.
Height of the image is 0.008 cm.