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  4. If the focal length of a double convex lens for red light is fR its focal length for the violet light is:

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Q. If the focal length of a double convex lens for red light is fR its focal length for the violet light is:

EAMCETEAMCET 2005Ray Optics and Optical Instruments

Solution:

In a double convex lens the speed of violet light is minimum while that of red light is maximum. So, the refractive index (n) of glass is maximum for violet light and minimum for red light $ ({{n}_{V}}-{{n}_{R}}). $ Hence according to the formula $ \frac{1}{f}=(n-1)\left( \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right) $ the focal length $ {{f}_{v}} $ of the lens for the violet light is least and the focal length $ {{f}_{R}} $ for the red light is largest i.e., $ {{f}_{R}}>{{f}_{V}}. $