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An achromatic lens of focal length 100 cm is made up of crown and flint glass lenses. Find the focal length of each lens. Given that for crown glass 1.5245, µv = µr = 1.5155 and for flint glass µv = 1.659 and µr = 1.641.

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The focal length of the combination of lens is given by 1/F = 1/f1 + 1/f2

If µ and µ’ are mean refractive indices for crown and flint glasses, respectively, then,

The dispersive powers ω and ω' for crown and flint glass, respectively, are 

To have an achromatic combination,

The achromatic doublet requires a convex lens of focal length 37.5 cm made of crown glass and a concave lens of focal length 60 cm made of flint glass.

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