The diameter of a plano-convex lens is 6 cm | vedclass

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(C) Given: Diameter of lens $= 6 \ cm$,so radius $a = 3 \ cm$. Thickness $t = 3 \ mm = 0.3 \ cm$. Speed of light in lens $v = 2 	imes 10^8 \ m/s$. Sp

Vedclass · Accepted Answer

$30$

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(C) Given: Diameter of lens $= 6 \ cm$,so radius $a = 3 \ cm$. Thickness $t = 3 \ mm = 0.3 \ cm$. Speed of light in lens $v = 2 	imes 10^8 \ m/s$. Speed of light in vacuum $c = 3 	imes 10^8 \ m/s$.Refractive index $\mu = \frac{c}{v} = \frac{3 	imes 10^8}{2 	imes 10^8} = 1.5$.For a spherical surface of radius $R$,the relationship between radius of aperture $a$,thickness $t$,and radius of curvature $R$ is given by $R^2 = a^2 + (R - t)^2$.$R^2 = a^2 + R^2 - 2Rt + t^2 \implies 2Rt = a^2 + t^2$.$R = \frac{a^2 + t^2}{2t} = \frac{3^2 + (0.3)^2}{2 	imes 0.3} = \frac{9 + 0.09}{0.6} = \frac{9.09}{0.6} = 15.15 \ cm$.Using the lens maker's formula for a plano-convex lens: $\frac{1}{f} = (\mu - 1) \left( \frac{1}{R} ight)$.$\frac{1}{f} = (1.5 - 1) \left( \frac{1}{15.15} ight) = 0.5 	imes \frac{1}{15.15} = \frac{1}{30.3}$.Thus,$f \approx 30 \ cm$.

The diameter of a plano-convex lens is $6 \ cm$ and its thickness at the center is $3 \ mm$. If the speed of light in the material of the lens is $2 \times 10^8 \ m/s$,the focal length of the lens is.......$cm$.

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