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A convex lens and a concave lens, each having same focal length of 25 cm, are put in contact to form a combination of lenses. The power in diopters of the combination is :-
A
25
B
50
C
Infinite
D
Zero
Detailed Solution
For thin lenses in contact, the powers add: $P = P_1 + P_2 = \dfrac{1}{f_1} + \dfrac{1}{f_2}$
Convex lens: $f_1 = +25$ cm. Concave lens: $f_2 = -25$ cm.
$P = \dfrac{1}{25} + \dfrac{1}{(-25)}$
$P = 0$
In diopters: $P_1 = \dfrac{100}{25} = +4$ D and $P_2 = -4$ D, so $P = 0$.
The combination behaves like a plane glass plate, with infinite focal length and zero power.
Convex lens: $f_1 = +25$ cm. Concave lens: $f_2 = -25$ cm.
$P = \dfrac{1}{25} + \dfrac{1}{(-25)}$
$P = 0$
In diopters: $P_1 = \dfrac{100}{25} = +4$ D and $P_2 = -4$ D, so $P = 0$.
The combination behaves like a plane glass plate, with infinite focal length and zero power.