Calculating Index of Refraction with Wavelength

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To calculate the critical angle for violet light (410 nm) entering water from air at a 75-degree incident angle, Snell's law is applied, yielding a critical angle of 46 degrees. The index of refraction for violet light in water can be determined using the Sellmeier equation, which relates wavelength to refractive index. The discussion emphasizes the importance of understanding how different wavelengths affect the index of refraction in various materials. Participants explore methods to calculate the index without relying on external sources. This approach enhances comprehension of light behavior at different wavelengths.
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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