I How can I derive this relation from Snell's law?

AI Thread Summary
The discussion centers on deriving a relationship from Snell's law regarding the refraction of white light into its colored components when transitioning from air to another medium. The author notes that for small angles of incidence, the difference in angles of refraction for blue and red light is proportional to the difference in their refractive indices. However, they express difficulty in deriving this proportionality using Snell's law. Participants are encouraged to share their attempts and insights to assist in clarifying this derivation. The conversation highlights the connection between refractive indices and the behavior of light in different media.
Ahmed1029
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Here, it's shown how white light, after passing from air to another medium, gets broken down into its constituent coloured rays. Each has its own refractive index in the medium, but it's only shown here red, blue and yellow. The auther comments on this image and says that, for small angles of incidence, the difference between the angles of refraction of blue and red is proportional to the difference of their respective indeces of refraction, which is trivially obtained from snell's law. I however can't derive this proportionality from Snell's law. Can someone help me?
 
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