Question

A convex lens of focal length $30cm$ is placed in contact with a concave lens of focal length $20cm$. What is the power of the combination of lens?

• A. $-0.0167D$
• B. $-10D$
• C. $-1.67D$
• D. $+1.67D$

Answer 1

The correct option is C $-1.67D$

Given:
Focal length of convex lens, $f_1=30cm$
Focal length of concave lens, $f_2=-20cm$
(Using new cartesian sign conventions, focal length of convex lens is positive and that of concave lens is negative)

Power of a lens in dioptre is reciprocal of its focal length in metre.
Power of convex lens, $P_1=\frac{1}{f_1}$
Power of concave lens, $P_2=\frac{1}{f_2}$

Power of combination of lenses in contact is the sum of individual powers. Hence, power of the effective lens is:
$P=P_1+P_2$
$P=\frac{1}{f_1}+\frac{1}{f_2}$
$P=\frac{1}{30/100}+\frac{1}{-20/100}$
$P=-1.67D$