Question

Two plano convex lenses of focal lengths$f_1$ and$f_2$ set for minimising spherical aberration are kept apart by 2 cm. If the equivalent focal length of combination is 10 cm, the values of $f_1$ and $f_2$ are :

• A. $18cm,16cm$
• B. $18cm,20cm$
• C. $20cm,22cm$
• D. $14cm,20cm$

Answer 1

The correct option is B $18cm,20cm$

$d=f_2-f_1$

$\Rightarrow f_2-f_1=2$ $\Rightarrow f_2=2+f_1$

$f_{eq}=\frac{f_1{f}_2}{f_1+f_2-d}=\frac{f_1{f}_2}{f_1+f_2-2}=10$

$\frac{\left(f_1\right)(2\times f_1)}{\left(2f_1\right)}=10$

$2+f_1=20$

$f_1=18cm$

$f_2=2+f_1=20cm$