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Q. A convex lens of focal length $40\, cm$ is in contact with a concave lens of focal length $25 \,cm$. The power of the combination, is

AIIMSAIIMS 1996Ray Optics and Optical Instruments

Solution:

Given: Focal length of a convex lens $\left(f_{1}\right)=40\, cm =0.4\, m$
and focal length of a concave lens $\left(f_{2}\right)=-25\, cm =-0.25 \,m$
(minus sign due to concave lens).
We know that relation for the focal length of
the combination of lenscs
$\frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}}$
$=\frac{1}{0 \cdot 4}+\frac{1}{-0 \cdot 25}$
$=2.5-4=-1 .5\, D$
or power $(P)=\frac{1}{f}=-1.5\, D$