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Question

The diameter of aperture of a plano-convex lens is 6 cm and its maximum thickness is 3 mm. If the velocity of light in the material of the lens is 2×108 m/s, its focal length is (approximately)

A
10 cm
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B
15 cm
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C
30 cm
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D
60 cm
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Solution

The correct option is C 30 cm
Diagram of the given lens:


Refractive index, μ of medium =Cv

μ=3×1082×108=1.5

Let, R is radius of curvature of lens.

Using geometry, we can write,

(R3)2+(30)2=R2

R2+96R+900=R2

909=6R

R=151.5 mm=15.15 cm

Applying lens maker formula,

1f0=(μ1)(1R1)

Substituting the value of μ and R,

1f0=0.5×115.15

f0=30.3030 cm

Hence, the option (c) is correct answer.


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