Question

Lenses applied in achromatic combination having dispersive power in ratio of $5:3$ if focal of length of the concave lens is $15cm$, then focal length of the other lens will be:

• A. $-9cm$
• B. $+9cm$
• C. $-12cm$
• D. $+12cm$

Answer 1

The correct option is B $+9cm$

Given,

${\omega }_1:{\omega }_2=5:3$

$f_1=-15cm$

We know that,

$\frac{{\omega }_1}{{\omega }_2}=-\frac{f_1}{f_2}$. . . . . . .(1)

$\frac{{\omega }_1}{{\omega }_2}=\frac{5}{3}$. . . . . .(2)

From equation (1) and equation (2), we get

$-\frac{f_1}{f_2}=\frac{5}{3}$

$f_2=-\frac{3f_1}{5}$

$f_2=-\frac{3\times (-15cm)}{5}=+9cm$

The correct option is B.