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What will be the position of the image, formed when an object of $3 cm$ height is placed at a distance of $10 cm$ in front of a converging mirror of focal length of $20 cm$ ?

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20 cm

behind the mirror

20 cm

in front of the mirror

10 cm

behind the mirror

10 cm

in front of the mirror

answer is A.

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Detailed Solution

The position of the image, formed when an object of

3 cm

height is placed at a distance of

10 cm

in front of a converging mirror of focal length of

20 cm

, will be

20 cm

behind the mirror.
Given,
Distance of the object from the mirror,

u = - 10 cm

(for a concave mirror)
The focal length (

f

) of the mirror,

f = - 20 cm

By using the mirror formula we know that,

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

\frac{1}{v} + \frac{1}{(- 10)} = \frac{1}{(- 20)}

\frac{1}{v} = \frac{1}{(- 20)} - \frac{1}{(- 10)}

\frac{1}{v} = \frac{1}{20}

v = + 20 cm

So, the position of the image formed will be

20 cm

behind the mirror( because of the positive sign ).

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