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When one surface of a thin lens is silvered, then the focal length F of the effective lens-mirror combination is expressed as,, where fi is the focal length of the lens or mirror to be repeated as many times as the refraction or reflection respectively is repeated.
Some Cases:

(i)Focal length of plano–convex lens when silvered at its plane surface

When an object is placed in front of such a lens. The ray first of all are refracted from the convex surface, then reflected from the polished plane surface and again refracted out from the convex surface. If and fm be the focal lengths of lens and mirror.


(ii) Focal length of plano –convex lens when silvered at convex surface

(iii) Focal length of convex lens where convex surface of radius R2 is silvered


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