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)

2D

Answer 2

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. $New power = \frac{4}{2}=2\, D$