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An object is placed at a distance of $10 cm$ from a concave mirror of a focal length of $20 cm$ . The image distance will be_

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10 cm

15 cm

20 cm

40 cm

answer is C.

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Detailed Solution

The image distance will be

20 cm .

Given data:
Focal length of the concave mirror,

f = - 20 cm

[Negative: as the mirror is concave]
Distance of object from the mirror,

u = - 10 cm

As we know the mirror formula ,

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

\Rightarrow \frac{1}{v} = \frac{1}{f} - \frac{1}{u}

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

\Rightarrow \frac{1}{v} = \frac{1}{- 20} - \frac{1}{- 10}

\Rightarrow \frac{1}{v} = \frac{- 1 + 2}{20}

\Rightarrow v = + 20 cm

A positive sign indicates that the image will be formed on the opposite side of the object.

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