Question

A convex lens of focal length 25 cm is placed coaxially in contact with a concave lens of focal length 20 cm. Determine the power of the combination. Will the system be converging or diverging in nature?

Answer 1

We have focal length of convex lens,

${\displaystyle f_1=+25cm=+0.25m}$and focal lenghth of conceave

lens, f₂ =-20 cm =-0.20 m

Equivalent focal length, ${\displaystyle f=\frac{1}{f_1} +\frac{1}{f_2} =\frac{1}{25}+\frac{1}{-20}=-\frac{1}{100}}$

∴ F =- 100 cm

Power of convex lens, ${\displaystyle P_1=\frac{1}{f_1}=\frac{1}{0.25}}$

Power of convex lens,${\displaystyle P_2=\frac{1}{f_2} = \frac{1}{-}0.20}$

Power of the combination,

${\displaystyle P=P_1+P_2=\frac{1}{0.25} +\frac{1}{-0.20}=\frac{100}{25}+\frac{100}{-20}=\frac{400-500}{100}=\frac{-100}{100} =-1D}$

The focal length of the combination =–1 m = –100 cm.

As the focal length is in negative, the system will be diverging in nature.