A concave lens has a focal length of 15 cm. At which distance should the object from the lens be placed so that it forms an image at 10 cm from the lens? Also, find the magnification of the lens.

The object should be placed

30 cm

from the lens on the left side and the magnification is

+ 0.33

.
Given,
Distance of image from the lens,

v = - 10 cm

Distance of the object from the lens,

u = ?

Focal length of the lens,

f = - 15 cm

By using the lens formula

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

\Rightarrow \frac{1}{- 10} - \frac{1}{u} = \frac{1}{- 15}

\Rightarrow \frac{1}{u} - \frac{1}{- 10} = \frac{1}{- 15}

\Rightarrow \frac{1}{u} = \frac{- 3 + 2}{30}

\Rightarrow u = - 30

Magnification,

m = \frac{v}{u}

\Rightarrow m = \frac{- 10}{- 30}

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

\Rightarrow m = + 0.33

A concave lens has a focal length of $15 cm$ . At which distance should the object from the lens be placed so that it forms an image at $10 cm$ from the lens? Also, find the magnification of the lens.