Question

An achromatic convergent lens of equivalent focal length +20 cm is made of two lenses (in contact) of materials having dispersive powers in the ratio of 1:2 and having focal lengths $f_1$ and $f_2$. The correct option is

• A. $f_1=$ 10cm, $f_2=$ 20cm
• B. $f_1=$ 20cm, $f_2=$ 10cm
• C. $f_1=$10cm, $f_2=$ -20cm
• D. $f_1=$ 20cm,$f_2=$ -10cm

Answer 1

Answer: (C)

$f_1=$10cm, $f_2=$ -20cm

Using, the additive property of powers of a lens,
$P=P_1+P_2$

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$

Also, the focal length is directly proportional to the dispersive power.

Hence, $\frac{f_1}{f_2}=-\frac{w_1}{w_2}$

Substituting the values as given in the question for $f=20$ and the given ratio to be given as $1:2$,

We get, $f_1=10$ and $f_2=-20$