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

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(C) The refractive index $n$ is given by $n = \frac{c}{v}$,where $c = 3 	imes 10^8 \ m/s$ is the speed of light in vacuum and $v = 2 	imes 10^8 \ m/

Vedclass · Accepted Answer

$30$

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(C) The refractive index $n$ is given by $n = \frac{c}{v}$,where $c = 3 	imes 10^8 \ m/s$ is the speed of light in vacuum and $v = 2 	imes 10^8 \ m/s$ is the speed in the medium.$n = \frac{3 	imes 10^8}{2 	imes 10^8} = 1.5$.Let $R$ be the radius of curvature of the curved surface. From the geometry of the lens,using the property of a chord in a circle: $r^2 = t(2R - t)$,where $r = 3 \ cm$ is the radius of the lens and $t = 3 \ mm = 0.3 \ cm$ is the thickness.$3^2 = 0.3(2R - 0.3) \Rightarrow 9 = 0.6R - 0.09 \Rightarrow 0.6R = 9.09 \Rightarrow R = 15.15 \ cm \approx 15 \ cm$.Using the lens maker's formula: $\frac{1}{f} = (n - 1)(\frac{1}{R_1} - \frac{1}{R_2})$.For a plano-convex lens,$R_1 = R = 15 \ cm$ and $R_2 = \infty$.$\frac{1}{f} = (1.5 - 1)(\frac{1}{15} - \frac{1}{\infty}) = 0.5 	imes \frac{1}{15} = \frac{1}{30}$.Therefore,$f = 30 \ cm$.

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

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