Question

A symmetric double convex lens is cut in two equal parts by a plane perpendicular to the principal axis. If the power of the original lens is 4D, the power of a cut lens will be

• A. 2D
• B. 3D
• C. 4D
• D. 5D

Answer 1

Answer: (A)

Biconvex lens is cut perpendicularly to the principal axis, it will become a plano- convex lens.
Focal length of biconvex lens
$ \frac{1}{f}= (n - 1) \bigg(\frac{1}{R_1}-\frac{1}{R_2}\bigg)$
$ \frac{1}{f}= (n - 1) \frac{2}{R} (\because R_1=R,R_2=-R)$
$ \Rightarrow \frac{1}{f}= \frac{R}{2} (n - 1) $...(i)
For plano-convex lens
$ \frac{1}{f_1}= (n - 1) \bigg(\frac{1}{R}-\frac{1}{\infty}\bigg)$
$ f_1= \frac{R}{(n - 1)} $...(ii)
Comparing Eqs. (i) and (ii),we see the focal length become
double.
As power of lens $ P \, \infty= \frac{1}{focal\, length}$
Hence, power will become half.
$ New power = \frac{4}{2}=2\, D$