Question

Two lenses of focal lengths $+10\text{cm}$ and $+15\text{cm}$ are put in contact to form an achromatic combination the ratio of their dispersive power is

• A. $\frac{+3}{2}$
• B. $\frac{-3}{2}$
• C. $\frac{+2}{3}$
• D. $\frac{-2}{3}$

Answer 1

The correct option is C $\frac{+2}{3}$

We know that the condition of achromatic is
$\frac{{\omega }_1}{f_1}+\frac{{\omega }_2}{f_2}=0$
$\Rightarrow \frac{{\omega }_1}{f_1}=\frac{-{\omega }_2}{f_2}$
$\Rightarrow \frac{{\omega }_1}{{\omega }_2}=\frac{-f_1}{f_2}$
$\Rightarrow \frac{{\omega }_1}{{\omega }_2}=\frac{-(+10)}{-15}=\frac{+2}{3}$