Question

Two thin lenses of same material separated by certain distance have an equivalent focal length of 50 cm. The combination satisfies the condition for no chromatic abberation and minimum spherical abberation. The focal length of the two lenses are

• A. 200/3cm, 100/3cm
• B. 100 cm, 100/3 cm
• C. 50 cm, 100 cm
• D. 50cm, $\frac{50}{3}$cm

Answer 1

The correct option is B 100 cm, 100/3 cm

$d=f_2-f_1$ (spherical abb)

$f_{eq}=50=\frac{f_1{f}_2}{f_1+f_2-d}$

$\frac{1}{f_1}+\frac{1}{f_2}=\frac{2a}{f_1{f}_2}$

$\Rightarrow f_1+f_2=2d$ (chromatic abb)

$f_2-f_1=d$

$2f_2=3d$

$f_1=\frac{d}{2}$

$f_2=\frac{3d}{2}$

$50=\frac{\frac{3d}{2}\times \frac{d}{2}}{d}=\frac{3d}{4}=50$

$\frac{3d}{2}=f_2=100$

$f_1=\frac{100}{3}$