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Question

The ratio to radii of curvature of a biconvex lens R1:R2 = 2 : 3. Its refractive index and focal length is 1.5 and 12 cm respectively. What is the value of R1? Consider R1 and R2 are positive and negative respectively.

A
5 cm
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B
10 cm
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C
15 cm
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D
20 cm
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Solution

The correct option is B 10 cm
We know by lens maker's formula,
1f=(μ1)[1R11R2]

where f if the focal length, μ is the refractive index and R1, R2 are the radii of curvature.

Given,
R1R2=23

Take R1 = x and R2 = 3x/2

112=(1.51)[1x+23x]112=0.5[53x]x=12×2.53=10 cm

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