A piano convex lens fits exactly into a piano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices μ$$1$$ and μ$$2$$ and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is

Question

A piano convex lens fits exactly into a piano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices μ$$1$$ and μ$$2$$ and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is

Infinity Learn · Accepted Answer

The combination of two lenses $$1$$ and $$2$$ is as shown in figure.∴   $$1f=1f1+1f2According$$ to lens maker's $$formula1f1=$$μ$$1$$−$$11$$∞−$$1R=$$μ$$1$$−$$1R$$ $$1f2=$$μ$$2$$−$$11$$−R−$$1$$∞ $$=$$μ$$2$$−$$1$$−$$1R=$$−μ$$2$$−$$1R$$ ∴  $$1f=$$μ$$1$$−$$1R$$−μ$$2$$−$$1R$$ $$1f=$$μ$$1$$−μ$$2R$$ $$f=R$$μ$$1$$−μ$$2$$

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A piano convex lens fits exactly into a piano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices μ1 and μ2 and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is

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