A biconvex lens has a focal length 2/3 times the radius of curvature of either surface. The refractive index of the lens material is :

1.75

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1.33

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1.5

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Solution

The correct option is D 1.75
Given: The focal length of the biconvex lens is $\frac{2}{3}$ times radius of curvature of each surface.

To find: The refractive index of the lens material.

The relation between the focal length and the radius of curvature for the lens is given by:
$\frac{1}{f} = (n - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

A biconvex lens has same radius of curvature for both surfaces.
$R_{1} = + R, R_{2} = - R$

and $f = \frac{2 R}{3}$

Substitute the values.
$\frac{3}{2 R} = (n - 1) (\frac{1}{R} + \frac{1}{R})$

$n = 1 + \frac{3}{4}$

$= 1.75$

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