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What will be the position of the image formed when an object is placed at $20 cm$ in front of a concave mirror of focal length $12 cm$ ?

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30 cm

40 cm

60 cm

10 cm

answer is A.

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Detailed Solution

The position of the image formed is at

30 cm

when an object is placed at

20 cm

in front of a concave mirror of focal length

12 cm

.
Given,

u = - 20 cm

f = - 12 cm

(Negative: as the mirror is concave)
By using the mirror formula, we can calculate the position of the image.

\frac{1}{f} = \frac{1}{v} + \frac{1}{u}

\Rightarrow \frac{1}{(- 12)} = \frac{1}{v} + \frac{1}{(- 20)}

\Rightarrow \frac{1}{v} = \frac{1}{20} - \frac{1}{12}

\Rightarrow \frac{1}{v} = \frac{3 - 5}{60}

\Rightarrow \frac{1}{v} = \frac{- 1}{30}

\Rightarrow v = - 30 cm

So, the position of the image formed is at

30 cm

in front of the mirror.

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