Silvering of Lens
Category : JEE Main & Advanced
On silvering the surface of the lens it behaves as a mirror. The focal length of the silvered lens is \[\frac{1}{F}=\frac{2}{{{f}_{l}}}+\frac{1}{{{f}_{m}}}\]
where \[{{f}_{l}}=\] focal length of lens from which refraction takes place (twice)
\[{{f}_{m}}=\] focal length of mirror from which reflection takes place.
(1) Plano convex is silvered
\[{{f}_{m}}=\frac{R}{2},\]\[{{f}_{l}}=\frac{R}{(\mu -1)}\] so \[F=\frac{R}{2\mu }\]
\[{{f}_{m}}=\infty ,\]\[{{f}_{l}}=\frac{R}{(\mu -1)}\] so \[F=\frac{R}{2\,(\mu -1)}\]
(ii) Double convex lens is silvered
Since \[{{f}_{l}}=\frac{R}{2\,(\mu -1)},\,{{f}_{m}}=\frac{R}{2}\] so \[F=\frac{R}{2\,(2\mu -1)}\]
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