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Question

# Diameter of a plano–convex lens is 6 cm and thickness at the centre is 3 mm. If the speed of light in the material of the lens is 2 108 m/sec, the focal length of the lens is

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

## The correct option is C 30 cmAccording to lens formula 1f=(μ−1)[1R1−1R2] The lens is plano-convex i.e., R1=R and R2=∞ Hence 1f=μ−1R⇒f=Rμ−1 Speed of light in medium of lens v=2×108m/s ⇒μ=cv=3×1082×108=32=1.5 If r is the radius and y is the thickness of lens (at the centre), the radius of curvature R of its curved surface in accordance with the figure is given by R2=r2+(R−y)2⇒r2−y2−2Ry=0 Neglecting y2; we get R=r22y=(62)22×0.3=15cm Hence f=151.5−1=30cm

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