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 $4\,D$ , 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
$\frac{1}{f}=(n-1)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$
$\frac{1}{f}=(n-1) \frac{2}{R}\,\,\left(\because R_{1}=R, R_{2}=-R\right)$
$\Rightarrow f=\frac{R}{2(n-1)}$ ...(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 $P \propto \frac{1}{\text { focal length }}$
Hence, power will become half.
New power $=\frac{4}{2}=2 D$