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>>Ray Optics and Optical Instruments
>>Combination of Mirror and Lenses
>> $The focal length of a convex lens is 10$

Question

The focal length of a convex lens is $10 c m$ and its refractive index is $1.5$ . If radius of one surface is $7.5 c m$ , the radius of curvature of the second surface will be

A

$7.5 c m$

B

$15 c m$

C

$75 c m$

D

$5 c m$

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Updated on : 2022-09-05

Solution

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Correct option is B)

According to lens maker formula,
$\frac{1}{f} = (μ_{g} - 1) \frac{1}{R _{1}} - \frac{1}{R _{2}}$
$\frac{1}{1 0} = 0.5 \frac{1}{R _{1}} - \frac{1}{R _{2}}$
$\frac{1}{5} = \frac{1}{R _{1}} - \frac{1}{R _{2}}$
$\frac{1}{5} = \frac{1}{7 5} - \frac{1}{R _{2}}$
$\frac{1}{R _{2}} = - \frac{1}{5} + \frac{1}{7 5}$
$\frac{1}{R _{2}} = \frac{- 3 + 2}{1 5}$
$R_{2} = 15 c m$

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