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Lens Maker's Formula

Arrange the f...

Question

Arrange the following data according to the increasing order of its focal length of given double covex lens of radius of curvature of the curved surfaces and corresponding refractive index of the material
a) $R_{1} = R_{2} = 2 c m$ $μ = 1.5$
b) $R_{1} = 20 c m, R_{2} = 10 c m$ $μ = 1.6$
c) $R_{1} = 20 c m, R_{2} = 30 c m$ $μ = 1.5$
d) $R_{1} = 20 c m, R_{2} = 40 c m$ $μ = 1.5$

c, b, a, d

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a, b, c, d

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b, c, d, a

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d, c, b, a

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Solution

The correct option is B a, b, c, d
$\frac{1}{f} = (μ - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

$f = \frac{(R_{1} R_{2})}{(R_{1} + R_{2}) (μ - 1)} (f o r c o n v e x)$

$f_{a} = \frac{2 \times 2 \times 2}{(4) (3)} = 2 / 3 c m$

$f_{b} = \frac{20 \times 10 \times 10}{6 \times 30} = \frac{200}{18} c m$

$f_{c} = \frac{20 \times 30 \times 2}{(50) (1)} = 24 c m$

$f_{d} = \frac{(20 \times 40 \times 2)}{(60) (1)} = \frac{80}{3}$

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