Calculating Index of Refraction with Wavelength

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SUMMARY

The discussion focuses on calculating the index of refraction for violet light (410 nm) as it transitions from air to water at an incident angle of 75 degrees. The critical angle for this transition is determined to be 46 degrees using Snell's law, expressed as n1sin(θ1)=n2sin(θ2). Participants highlight the importance of understanding the wavelength-dependent nature of the index of refraction and suggest using the Sellmeier equation for self-calculation of the index without external references.

PREREQUISITES
  • Understanding of Snell's Law (n1sin(θ1)=n2sin(θ2))
  • Familiarity with the concept of the index of refraction
  • Knowledge of wavelength and frequency relationships (n=c/v)
  • Basic understanding of the Sellmeier equation for calculating refractive indices
NEXT STEPS
  • Research the Sellmeier equation for calculating the index of refraction
  • Study the wavelength dependence of refractive indices in different materials
  • Explore advanced applications of Snell's Law in optics
  • Learn about critical angles and total internal reflection in various media
USEFUL FOR

Students in physics or optics courses, educators teaching light refraction concepts, and anyone interested in the practical applications of Snell's Law and the Sellmeier equation.

waley

Homework Statement


A beam of white light goes from air into water at an incident angle of 75 deg. What is the critical angle that the violet (410 nm) parts of the light is refracted?

Homework Equations


n1sin(θ1)=n2sin(θ2)
n=c/v
c=λf

The Attempt at a Solution


So sure, I get that the answer is supposed to be 46 degrees. I got this by looking up the index of refraction of violet light in water then using Snell's law. But I do know that the wavelengths of the same wave differ in different materials, and the problem gives us the wavelength of violet light. Is there a way I can calculate this index by myself without having to look it up?
 
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