A plano-convex lens (mu = 1.5) has a radius o | vedclass

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(B) The focal length of a silvered lens is given by the formula $\frac{1}{F} = \frac{2}{f_l} + \frac{1}{f_m}$,where $f_l$ is the focal length of the l

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$10$

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(B) The focal length of a silvered lens is given by the formula $\frac{1}{F} = \frac{2}{f_l} + \frac{1}{f_m}$,where $f_l$ is the focal length of the lens and $f_m$ is the focal length of the mirror.For a plano-convex lens,the focal length $f_l$ is given by $\frac{1}{f_l} = (\mu - 1)(\frac{1}{R_1} - \frac{1}{R_2})$.Here,$R_1 = 10 \; cm$ and $R_2 = \infty$,so $\frac{1}{f_l} = (1.5 - 1)(\frac{1}{10} - 0) = \frac{0.5}{10} = \frac{1}{20}$. Thus,$f_l = 20 \; cm$.The silvered plane surface acts as a plane mirror,so its focal length $f_m = \infty$.Therefore,$\frac{1}{F} = \frac{2}{20} + \frac{1}{\infty} = \frac{1}{10} + 0 = \frac{1}{10}$.Hence,$F = 10 \; cm$.

$A$ plano-convex lens $(\mu = 1.5)$ has a radius of curvature of $10 \; cm$. It is silvered on its plane surface. Find the focal length after silvering. (in $; cm$)

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