Question

Focal lengths of two lenses are $f$ and $f$ and dispersive powers of their materials are $\omega$ and $\omega$. Two from achromatic combination from these, which relation is correct?

• A. $\omega ={\omega }_0,{\omega }^{\prime }=2{\omega }_0,f^{\prime }=2f$
• B. $\omega ={\omega }_0,{\omega }^{\prime }=2{\omega }_0,f^{\prime }=-2f$
• C. $\omega ={\omega }_0,{\omega }^{\prime }=2{\omega }_0,f^{\prime }=f/2$
• D. $\omega ={\omega }_0,{\omega }^{\prime }=2{\omega }_0,f^{\prime }=-f/2$

Answer 1

The correct option is B $\omega ={\omega }_0,{\omega }^{\prime }=2{\omega }_0,f^{\prime }=-2f$

Let first lens focal length= $f_0$

dispersive power $={\omega }_0$

Second lens focal length $=f^{\prime }$

dispersive power $={\omega }^{\prime }$

formula for achromatic combination

$\frac{{\omega }_1}{f_1}+\frac{{\omega }_2}{f_2}=0$

if $\omega ={\omega }_0{\omega }^{\prime }=2{\omega }_0{f}^1=-2f$

$\frac{2{\omega }_0}{-2f}+\frac{{\omega }_0}{f}=0$

So option (B) is correct