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