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  4. The dispersive powers of glasses of lenses used in an achromatic pair are in the ratio 5: 3. If the focal length of the concave lens is 15 cm, then the nature and focal length of the other lens would be

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Q. The dispersive powers of glasses of lenses used in an achromatic pair are in the ratio $5: 3$. If the focal length of the concave lens is $15\, cm$, then the nature and focal length of the other lens would be

AIIMSAIIMS 2011

Solution:

Condition for achromatic combination
$\frac{\omega}{\omega'}=-\frac{f}{f'}$
$\frac{5}{3}=\frac{-(-15)}{f'}$
$\Rightarrow f'=9\, cm$
Focal length is positive, so it is convex