Question

The dispersive power of the materials of the two lenses are in the ratio 4:3. If the achromatic combination of these two lenses in contact is a convex lens of focal length 60 cm, then the focal length of the component lenses are

• A. 20 cm and +25 cm
• B. 20 cm and -25 cm
• C. 15 cm and +20 cm
• D. 15 cm and -20 cm

Answer 1

The correct option is D 15 cm and -20 cm

For an achromatic combination,
$\frac{f_1}{w_1}+\frac{f_2}{w_2}=0$

Also, the effective focal length of the combination will be:
$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$

Solving these simultaneously and substituting the values, the obtained focal lengths are, $f_o=15$ and $f_e=-20$