The diameter of a plano-convex lens is 6 cm and its thickness at the centre is 3 mm. What is the focal length of the lens if the speed of light in the material of lens is $2 \times 10^{8} m / s$ ?

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15 cm

20 cm

25 cm

30 cm

answer is D.

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Detailed Solution

$\begin{array}{l} R^{2} = (R - t)^{2} + \frac{d^{2}}{4} \\ R^{2} = R^{2} + t^{2} - 2 R t + \frac{d^{2}}{4} \\ \Rightarrow R = \frac{d^{2}}{8 t} = \frac{6^{2}}{8 \times 0.3} = 15 cm \\ f = (\frac{R}{μ - 1}) = \frac{15}{1.5 - 1} = 30 cm \end{array}$

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