# JEE Main & Advanced Physics Ray Optics Silvering of Lens

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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