Question

If a convex lens of focal length $80cm$ and a concave lens of focal length $50cm$ are combined together, what will be their resultant power?

• A. $+0.65D$
• B. $-0.65D$
• C. $+0.75D$
• D. $-0.75D$

Answer 1

Answer: (D)

The power of a thin lens is equal to the reciprocal of its focal length (f) measured in metres. Power of the combination is given by
$P=\frac{1}{f(metre)}$
Combined focal length is
$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$
Given, $f_1=80cm,f_2=-50cm$ (concave)
$\therefore$ $\frac{1}{f}=\frac{1}{80}-\frac{1}{50}$
$=-\frac{30}{4000}$
$\Rightarrow$ $f=-\frac{4000}{30}cm$
$\therefore$ $power=-\frac{100}{400/3}$
$=\frac{-3}{4}=-0.75D$
As focal length of combination is negative, hence combination behaves like a diverging lens.