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Question:
If the refractive index of a medium for red and violet light are r & v respectively prove that r < v
Answer:

Refractive index - sin i/sin r

In case of red light, which has higher frequency than the violet light, when passing through a medium does ot bend by a graeter angle compared to violet light which has lower frequency. Violet light bends more and thus its angle of refraction compared to red light is less. This will be clear if you understand the angles of incidence and refraction as shown below.

Thus sin i/sin r is more for violet light than for red light. Thus, r < v.

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