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

Updated On: Jun 17, 2023

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The Correct Option is A

Solution and Explanation

Let P₁ and P₂ are the power of lenses.
P_eq = P₁ + P₂
Given, P_eq = 9
P₁ + P₂= 9 ………………(1)
Power of lenses when distance is separated by d = 0.2 m ,
P^'_eq= P₁ + P₂ − dP₁P₂
Given, P^'_eq=\(\frac {27}{5}\)
\(\frac {27}{5}\) = 9 − 0.2 P₁P₂
on solving P₁P₂=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

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Concepts Used:

Spherical Lenses

Lenses that are made by combining two spherical transparent surfaces are called spherical lenses. In general, there are two kinds of spherical lenses. Lenses that are made by joining two spherical surfaces that bulge outward are convex lenses, whereas lenses that are made by joining two spherical surfaces that curve inward are concave lenses.

Properties of Convex lens:

In this, the lenses are thicker in the middle and thinner at the edges.
They have a positive focal length.
It intersects the incident rays towards the principal axis
These lenses are used in the camera, focus sunlight, projector microscope, simple telescope, overhead projector, magnifying glasses, etc.

Properties of Concave lens:

These lenses are thinner in the middle and thicker at the edges.
They have a negative focal length.
It parts the incident rays away from the principal axis.
These are used in the glasses, spy holes, some telescopes in the doors, etc.