A double convex lens has focal length $25 c m$ . The radius of curvature of one of the surface is double of the other. Find the radii, if the refractive index of the material of the lens is $1.5$ .

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Solution

For the double convex lens
$f = 25 c m, R_{1} = R$ and $R_{2} = - 2 R$ (sign convention)

$\frac{1}{f} = (μ - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

$\Rightarrow \frac{1}{25} = (15 - 1) (\frac{1}{R} - \frac{1}{- 2 R}) = 0.5 (\frac{3 R}{2})$

$\Rightarrow \frac{1}{25} = \frac{3}{4} \frac{1}{R} \Rightarrow R = 18.75 c m$

$R_{1} = 18.75 c m, R_{2} = 2 R = 37.5 c m$

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