Question

An achromatic convergent system of focal length $+20$cm is made of two lenses(in contact) of materials having dispersive powers in the ratio $1:2$. Their focal lengths must be respectively.

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

Answer 1

The correct option is A $10$cm, $-20$cm

$\frac{{\omega }_1}{f_1}+\frac{{\omega }_2}{f_2}=0$
$\Rightarrow \frac{\omega }{f}+\frac{2\omega }{f_2}=0$
$f_2=-2f_1$
$\therefore \frac{1}{f_1}+\frac{1}{f_2}=\frac{1}{F}$
$\Rightarrow \frac{1}{f_1}-\frac{1}{2f_1}=\frac{1}{20}$
$\Rightarrow \frac{1}{2f_1}=\frac{1}{20}$
$\Rightarrow f_1=10cm,f_2=-20$cm.