Question

If a convex lens of focal length $75cm$ and a concave lens of focal length $50cm$ are combined together, what will be their resulting power ?

• A. $-6.6D$
• B. $+0.66D$
• C. $+6.6D$
• D. $-0.66D$

Answer 1

Answer: (D)

Convex lens is a converging lens while concave lens is a diverging one.
Power of a lens is defined as reciprocal of focal length measured in metres.
$\therefore P=\frac{1}{f\left(inm\right)}D$ or $P=\frac{100}{f\left(cm\right)}D$
Given, $f_1=+75cm$, $f_2=-50cm$
$\therefore \frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$
$=\frac{1}{75}-\frac{1}{50}$
$=\frac{2-3}{150}=-\frac{1}{50}$
$\Rightarrow f=-150cm$
$\therefore$ Power $=\frac{100}{f}=-\frac{100}{150}$
$=-0.66D$
Since, focal length of combined lens is negative, it behaves as a diverging lens.