How far should an object be placed from the pole of a converging mirror of focal length 20cm to form a real image of the size exactly $\frac {1}{4}th$ the size of the object?

Focal length of the mirror, $f$ = 20 cm

Magnification, $m$ = $-\frac {1}{4}$

To find: Distance of the object $(u)$ from the mirror.

Solution:

From the magnification formula, we know that-

$m=-\frac{v}{u}$

Substituting the given values in the magnification formula we get-

$-\frac {1}{4}=-\frac{v}{u}$

$v=\frac {u}{4}$

Now, from the mirror formula, we know that-

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

Substituting the given values in the mirror formula we get-

$\frac{1}{-20}=\frac{1}{\frac{u}{4}}+\frac{1}{u}$

$\frac{1}{-20}=\frac{4}{u}+\frac{1}{u}$

$\frac{1}{-20}=\frac{4+1}{u}$

$\frac{1}{-20}=\frac{5}{u}$

$u=-100cm$

Thus, the object should be placed in front of the concave mirror at a distance of 100 cm. The negative sign implies that it is placed in front of the mirror (on the left).

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Updated on: 10-Oct-2022

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