Question

Two thin lenses have a combined power of +9D. When they are separated by a distance of 20 cm, then their equivalent power becomes +27/5 D. Their individual power (in dioptre) is

• A. 3,6
• B. 1,8
• C. 2,7
• D. 4,5

Answer 1

Answer: (A)

3,6

Answer 2

Let P1 and P2 are the power of lenses.
Peq​ = P1 + P2
Given, Peq​ = 9
​P1 + P2 = 9 ………………(1)
Power of lenses when distance is separated by d = 0.2 m ,
P'eq = P1​ + P2​ − dP1​P2​
Given, P'eq =$\frac {27}{5}$
$\frac {27}{5}$ ​= 9 − 0.2 P1​P2​
on solving P1​P2​=18
P2 = $\frac {18}{P_1}$
From eq (1)
P1 + $\frac {18}{P_1}$ = 9 …………(2)
P12 + 18 = 9 P1
P12​ − 9P1​+18=0
on solving P1​ = 6 D
Now from eq (1)
6 + P2 = 9
P2 = 9 - 6
P2 = 3 D
Therefore the correct option is (A) 3,6