Question

USCULO
Example 10.3
A concave lens has focal length of 15 cm. At what 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 produced by the lens.
Solution​

Answer 1

Given :

• The focal length of a concave lens (f) = - 15 cm.
• Distance of the Image (v) = - 10 cm.

To Find :

• Distance of the object (u).
• Magnification produced by the lens (M).

Solution :

• Finding the distance of the object.

$\underline{\boxed{\bf{Using \; Formula\;:\; \dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u} }}}$

$\longrightarrow \sf{ \dfrac{1}{-15} = \dfrac{1}{-10} - \dfrac{1}{u}}$

$\longrightarrow \sf{ \dfrac{1}{u} = - \dfrac{1}{10} + \dfrac{1}{15}}$

$\longrightarrow \sf{ \dfrac{- 3 + 2}{30} = \dfrac{1}{u}}$

$\longrightarrow \sf{\cancel{\dfrac{-1}{30}} = \dfrac{1}{u}}$

$\longrightarrow \sf{u = - 30}$

Hence, the distance of the object = 30 cm.

• Finding magnification produced by the lens.

$\underline{\boxed{\bf{Using \; Formula\;:\; M = \dfrac{v}{u} }}}$

$\longrightarrow \sf{ M = \dfrac{- 10}{- 30} }$

$\longrightarrow \sf{ M = \dfrac{1}{3} }$

Hence, the Magnification produced by the lens = 0.33