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

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SUMMARY

This discussion focuses on deriving the relationship between the angles of refraction of different colors of light as described by Snell's Law. The author highlights that when white light transitions from air to another medium, it separates into its constituent colors, each with distinct refractive indices. Specifically, the relationship between the angles of refraction for blue and red light is proportional to the difference in their refractive indices, a concept derived from Snell's Law. Participants seek assistance in mathematically deriving this proportionality.

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  • Understanding of Snell's Law and its mathematical formulation.
  • Knowledge of refractive indices for different wavelengths of light.
  • Basic principles of optics, particularly light refraction.
  • Familiarity with angle measurements in physics.
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  • Research the mathematical derivation of Snell's Law.
  • Explore the concept of refractive index variations with wavelength.
  • Study the phenomenon of dispersion in optics.
  • Learn about the application of Snell's Law in different media transitions.
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Students of physics, optics enthusiasts, and educators seeking to deepen their understanding of light behavior during refraction and its mathematical implications.

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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