A plano-convex lens has a diameter of 6, cm a | vedclass

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(C) Given: Diameter $D = 6\, cm$,so radius $a = 3\, cm = 0.03\, m$. Thickness at center $t = 3\, mm = 0.003\, m$.Speed of light in lens $v = 2 	imes

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$30$

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(C) Given: Diameter $D = 6\, cm$,so radius $a = 3\, cm = 0.03\, m$. Thickness at center $t = 3\, mm = 0.003\, m$.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 $\mu = c/v = (3 	imes 10^{8}) / (2 	imes 10^{8}) = 1.5$.For a plano-convex lens,the radius of curvature $R$ is related to the radius $a$ and thickness $t$ by the formula: $R = (a^2 + t^2) / (2t)$.Since $t$ is very small,$t^2$ is negligible,so $R \approx a^2 / (2t) = (3^2) / (2 	imes 0.3) = 9 / 0.6 = 15\, cm$.The focal length $f$ is given by the Lens Maker's Formula: $1/f = (\mu - 1)(1/R_1 - 1/R_2)$.Here $R_1 = R = 15\, cm$ and $R_2 = \infty$.$1/f = (1.5 - 1)(1/15 - 0) = 0.5 / 15 = 1 / 30$.Therefore,$f = 30\, cm$.

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

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