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Determine the focal length of a concave ...

Determine the focal length of a concave spherical mirror which is manufactured in the form of a thin symmetric biconvex glass lens one of whose surfaces is silvered. The curvature radius of the lens surface is `R = 40 cm`.

Text Solution

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`C` is the centre of curvature of the silvered surface and `O` is the effective centre of the equivalent mirror in the sence that an object at `O` forms a coincident image. From the figure, using the fromula fro refraction at a spherical surface, we have,
`(n)/(-R) - (1)/(2f) = (n - 1)/(R )` or `f = (-R)/(2(2n - 1))`
(In our convention `f` is `-ve`).
Substituation gives `f =- 10 cm`.
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