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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.
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Solution
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.
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