Question

For achromatic combination of lenses, if we use two lenses of focal length and $ f $ respectively, dispersive powers $ \omega $ and $ \omega , $ then:

• A. $\omega=\omega_{0}, \omega'=2 \omega_{0}, f'=2 f$
• B. $\omega=\omega_{0}, \omega'=2 \omega_{0}, f'=-2 f$
• C. $\omega=\omega_{0}, \omega'=2 \omega_{0}, f'=f / 2$
• D. $\omega=\omega_{0}, \omega'=2 \omega_{0} f'=-f / 2$

Answer 1

Answer: (B)

The condition of achromatic combination is
$\frac{\omega}{\omega'}=-\frac{f}{f'}$
This is satisfied if
$\omega=\omega_{0}, \omega'=2 \omega_{0}$ and $f=2 f$
So that, $\frac{\omega_{0}}{2 \omega_{0}}=\frac{-f}{-2 f}$
$\Rightarrow \frac{1}{2}=\frac{1}{2}$