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  4. In Ramadens eye-piece, the two plano-convex lenses each of focal length/, are separated by a distance 12 cm. The equivalent focal length (in cm) of the eye lens:

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Q. In Ramadens eye-piece, the two plano-convex lenses each of focal length/, are separated by a distance 12 cm. The equivalent focal length (in cm) of the eye lens:

EAMCETEAMCET 2006

Solution:

Ramsdens eye-piece consists of two co-axial plano-convex lenses of focal length $ f $ and $ {{f}_{1}} $ separated by a distance $ \frac{2f}{3}, $ $ \frac{2f}{3}=12 $ $ \Rightarrow $ $ f=\frac{12\times 3}{2}=18\,cm $ So, equivalent focal length $ \frac{1}{F}=\frac{1}{f}+\frac{1}{f}-\frac{d}{{{f}^{2}}} $ $ =\frac{1}{18}+\frac{1}{18}-\frac{12}{{{(18)}^{2}}} $ $ =\frac{1}{9}-\frac{1}{27} $ $ =\frac{2}{27} $ $ \therefore $ $ f=\frac{27}{2}=13.5\,cm $