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 $\frac{1}{f}=(n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$ $\frac{1}{f}=(n-1)\frac{2}{R}$ $(\because R_1=R,R_2=-R)$ $\Rightarrow$ $f=\frac{R}{2(n-1)}$ ? (i) For plano-convex lens $\frac{1}{f_1}=(n-1)\left(\frac{1}{R}-\frac{1}{\infty }\right)$ $f_1=\frac{R}{(n-1)}$ ? (ii) Comparing Eqs. (i) and (ii), we see that focal length becomes double. As power of lens $P\propto \frac{1}{focallength}$ Hence, power will become half. New power $=\frac{4}{2}=2D$