Question

An achromatic convergent lens of focal length 20 cms 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${}_2$. Which of the following is true?

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

Answer 1

The correct option is A $f_1=10cms,f_2=20cms$

$\frac{f_1}{f_2}=-\frac{{\omega }_1}{{\omega }_2}=-\frac{1}{2}$

$\therefore f_2=-2f_1$

As $\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}$

$\therefore \frac{1}{20}=\frac{1}{f_1}-\frac{1}{2f_1}=\frac{1}{2f_1}\therefore f_1=10cm$

$f_2=-20cm$