Examples
Ex 1:
1. A convex lens of focal length 25 cm is placed in contact with a concave lens of focal length 40 cm. Find:
(i) power of each of the lens
(ii) power of combination
(iii) focal length of combination
(iv) nature of combination.
Sol:
(i) Power of convex lens = 100/25
= + 4D
Power of concave lens = 100/40
= – 2.5 D
(ii) Power of combination P = P1 + P2
= (+ 4D) + (– 2.5 D)
= + 1.5 D.
(iii) Focal length of combination f (in cm) = 100/P
= 100/1.5
= +66.67 cm.
(iv) As the power of the combination is positive, therefore combination behaves like a convex.
Ex 2:
A convex lens of a focal length of 20 cm is placed in contact with a concave lens of focal length 40 cm. Find:
(i) power of each lens
(ii) power of combination
(iii) nature of the combination
(iv) focal length of combination.
Sol:
(i) Power of convex lens = 100/20
= + 5 D
Power of concave lens = 100/40
= – 2.5 D
(ii) Power of combination P = P1 + P2
= (+ 5 D) + (– 2.5 D)
= + 2.5 D.
(iii) As the power of the combination is positive, therefore combination behaves like a convex.
(iv) Focal length of combination f (in cm) = 100/P
= 100/2.5
= + 40 cm.
Ex 3:
A concave lens of power – 2D is placed in contact with a convex lens of focal length 125 cm. Find:
(i) power of combination
(ii) nature of the combination
(iii) focal length of combination.
Sol:
(i) Given the Power of concave lens = – 2D
Power of convex lens = 100/125
= + 0.8 D
(ii) Power of combination P = P1 + P2
= (+ 0.8 D) + (– 2 D)
= – 1.2 D.
As the power of the combination is negative, therefore combination behaves like a concave.
(iii) Focal length of combination f (in cm) = 100/P
= 100/– 1.2
= – 83.33 cm.