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Image Formation in Concave Mirror

The object AB...

Question

The object $A B$ is placed on the axis of a concave mirror of focal length $10 cm$ . End $A$ of the object is $30 cm$ from the mirror. Find the length of the image if the length of the object is $5 cm$ .

1 cm

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2 cm

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3 cm

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4 cm

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Solution

The correct option is A $1 cm$
For end $A$ ,
$u = - 30 cm$
$f = - 10 cm$
So, $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
$\Rightarrow \frac{1}{v} - \frac{1}{30} = \frac{- 1}{10}$
$\Rightarrow \frac{1}{v} = \frac{- 1}{15}$
$\Rightarrow v = - 15 cm$
Similarly, for end $B$ ,
$u = - (30 + 5) = - 35 cm$
$f = - 10 cm$
So, $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
$\Rightarrow \frac{1}{v} - \frac{1}{35} = \frac{- 1}{10}$
$\Rightarrow \frac{1}{v} = \frac{- 1}{14}$
$\Rightarrow v = - 14 cm$
Now, size of image $= | - 15 - (- 14) | = 1 cm$

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