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At what distance should an object be placed from a convex lens of focal length $18 cm$ to obtain an image $24 cm$ from it on the other side? What will be the magnification produced in this case?

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u = 72 cm, m = + 1 / 5

u = - 72 cm, m = - 1 / 3

u = 72 cm, m = + 1 / 3

None of these

answer is B.

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Detailed Solution

The object should be placed at

- 72 cm

from the lens and the magnification is

- 0.33

.
Given,
Distance of image from the lens,

v = 24 cm

Distance of the object from the lens,

u = ?

The focal length of the lens,

f = 18 cm

By using the lens formula

\Rightarrow \frac{1}{f} = \frac{1}{v} - \frac{1}{u}

\Rightarrow \frac{1}{24} - \frac{1}{u} = \frac{1}{18}

\Rightarrow \frac{1}{u} = \frac{1}{24} - \frac{1}{18}

\Rightarrow \frac{1}{u} = \frac{18 - 24}{24 \times 18}

\Rightarrow u = - 72 cm

Magnification,

m = \frac{v}{u}

\Rightarrow m = \frac{24}{- 72}

\Rightarrow m = - \frac{1}{3}

\Rightarrow m = - 0.33

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