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An object placed $20 cm$ in front of a mirror is found to have an image $15 cm$ behind the mirror. Calculate the focal length.

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60 cm

70 cm

80 cm

90 cm

answer is A.

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Detailed Solution

An object placed

20 cm

in front of a mirror is found to have an image

15 cm

behind the mirror. Its focal length is

60 cm

.
Given,
Object distance

u = - 20 cm

Image distance

v = + 15 cm

(positive: as the image is forming behind the mirror)
Let the focal length is

= f

Now, applying the Mirror’s formula

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

\Rightarrow \frac{1}{f} = \frac{1}{15} + \frac{1}{- 20}

\Rightarrow \frac{1}{f} = \frac{4 - 3}{60}

\Rightarrow \frac{1}{f} = \frac{1}{60}

\Rightarrow f = + 60 cm

As the focal length is positive, the mirror will be a convex mirror.

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