Question

A biconvex lens has a focal length $f$. It is cut into two parts along a line perpendicular to principal axis. The focal length of each part will be

• A. $\frac{f}{2}$
• B. $f$
• C. $\frac{3f}{2}$
• D. $2f$

Answer 1

The correct option is D $2f$

Applying the lens maker's formula
$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$
For biconvex lens
$R_1=R$ and $R_2=-R$
Hence
$\frac{1}{f}=\frac{2(\mu -1)}{R}$----(1)
After cutting the lens
$R_2=\infty$
Putting this value in the lens maker's formula
$\frac{1}{f^{\prime }}=\frac{\mu -1}{R}$-----(2)
From equation (1) and (2)
$f^{\prime }=2f$

Why this question? Caution- If the centre of the curved surface is to the right for a incident ray travelling rightwards- then R is positive and vice versa.