A plano-convex lens when silvered in the plane side behaves like a concave mirror of focal length $30cm$. However, when silvered on the convex side it behaves like a concave mirror of focal length $10\ cm$. Then the refractive index of its material will be

Question

Dr. Abubacker · Accepted Answer

(d) Here $\frac{1}{F} = \frac{2}{f} + \frac{1}{f_{m}}$
Plano-convex lens silvered on plane side has $f_{m} = \infty$
$	herefore\frac{1}{F} = \frac{2}{f} + \frac{1}{\infty} \Rightarrow \frac{1}{30} = \frac{2}{f} \Rightarrow f = 60\ cm$
Plano-convex lens silvered on convex side has $f_{m} = \frac{R}{2}$
$	herefore\frac{1}{F} = \frac{2}{f} + \frac{2}{R} \Rightarrow \frac{1}{10} = \frac{2}{60} + \frac{2}{R} \Rightarrow R = 30\ cm$
Now using $\frac{1}{f} = (\mu - 1)\left( \frac{1}{R} ight)$, we get $\mu = 1.5$

Q. A plano-convex lens when silvered in the plane side behaves like a concave mirror of focal length $30cm$. However, when silvered on the convex side it behaves like a concave mirror of focal length $10\ cm$. Then the refractive index of its material will be

Explanation

Reviewed by Dr. Abubacker

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