Question

The focal length of the field lens (which is an achromatic combination of two lenses) of telescope is $90 \,cm$. The dispersive powers of the two lenses in the combination are $0.024$ and $0.036$. The focal lengths of two lenses are

• A. 30 cm and 60 cm
• B. 30 cm and -45 cm
• C. 45 cm and 90 cm
• D. 15 cm and 45 cm

Answer 1

Answer: (B)

For achromatic combination
$\frac{f_{1}}{f_{2}}=-\frac{\omega_{2}}{\omega_{1}}=-\frac{0.036}{0.024}=-\frac{3}{2}$
and $\frac{1}{f_{1}}-\frac{1}{f_{2}}=\frac{1}{90}$
Solving above equations we get
$f_{1}=30 \,cm$, $f_{2}=-45 \,cm$