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A concave spherical mirror produces $- \frac{1}{2}$ magnification when an object is placed at a distance of $50 cm$ from the mirror. Where the object should be placed to get the magnification of $- \frac{1}{5}$ ?

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125 cm

100 cm

324 cm

129 cm

answer is A.

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Detailed Solution

The object should be placed at

125 cm

from the mirror to get the magnification of

- \frac{1}{5}

.
Given,
As the object is placed at a distance of

50 cm

from the mirror,

u = - 50 cm

m = - 1 / 2

Substituting these values in magnification formula, we get

m = - \frac{v}{u}

\Rightarrow - \frac{1}{2} = - \frac{v}{(- 50)}

\Rightarrow v = - 25 cm

Now, substituting the value of

v

in magnification formula for calculating the distance of the object when the magnification produced is

- \frac{1}{5}

, we get

m = - \frac{v}{u}

\Rightarrow - \frac{1}{5} = - \frac{(- 25)}{u}

\Rightarrow u = - 125 cm

Therefore, the object should be placed at a distance of

125 cm

from the mirror.

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