Question

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

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

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}}=80\,cm,\,{{f}_{2}}=-50\,cm $ (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.