Question

Two convex lenses of powers 4 d and 6 d are separated by a distance of 1 6 m . The power of the optical system so formed is

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