Question

Two thin convex lenses of power 4D and 6D are placed co-axially at a distance of 20cm apart.find the focallength and power of the combination of lense

Answer 1

if we assume that $f_1$ be the focal length of first convex lens and $f_2$ be the focal length of second convex lens.

use formula, $P=P_1+P_2-d.P_1.P_2$

here P is the combined power of the optical system $P_1$ and $P_2$ are the powers of the individual lenses and 'd' is the distance.
here, $P_1$ = 4D
$P_2$ = 6D
and d = 20cm = 0.2m

so, P = 4 + 6 - 0.2 × 4 × 6
hence, P = 10 - 4.8 = 5.2D

focal length , $\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1.f_2}$

$f_1$ = 1/4 = 25cm
$f_2$ = 1/6 = 50/3cm

now, 1/f = 1/25 + 3/50 - 20 × 3 /(25 × 50)
= 2/50 + 3/50 - 12/250
= (10 + 15 - 12)/250
= 13/250

hence, f = 250/13 = 19.23cm