Question

The figure shows an equiconvex lens of focal length $f.$ If the lens is cut along PQ, the focal length of each half will be

• A. $\frac{f}{2}$
• B. $f$
• C. $2f$
• D. $4f$

Answer 1

Answer: (C)

According to Lens Makers formula,
$\frac{1}{f}=(\mu -1)\left(\frac{1}{R}-\frac{1}{R}\right)$

$\Rightarrow$ $\frac{1}{f}=(\mu -1)\left(\frac{2}{R}\right)$ ..... (i)
On cutting, $\frac{1}{f}=(\mu -1)\left(\frac{1}{R}-\frac{1}{\infty }\right)$
$\frac{1}{f}=(\mu -1)\left(\frac{1}{R}\right)$ ..... (ii)
From Eqs. (i) and (ii), we get
$f=2f$