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
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
- 3,6
- 1,8
- 2,7
- 4,5
The Correct Option is A
Solution and Explanation
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 − 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.