Calculating Index of Refraction with Wavelength

In summary, the critical angle for the violet light (410 nm) to be refracted in water is 46 degrees. This can be calculated using the formula n1sin(θ1)=n2sin(θ2) and looking up the index of refraction for violet light in water. Alternatively, one can use the Sellmeier equation to calculate the index of refraction for a specific wavelength.
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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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1. How do you calculate the index of refraction with wavelength?

To calculate the index of refraction with wavelength, you need to divide the speed of light in a vacuum by the speed of light in the medium at the given wavelength. The resulting value is the index of refraction at that specific wavelength.

2. What is the formula for calculating the index of refraction with wavelength?

The formula for calculating the index of refraction with wavelength is n = c/v, where n is the index of refraction, c is the speed of light in a vacuum, and v is the speed of light in the medium at the given wavelength.

3. What is the relationship between wavelength and index of refraction?

The index of refraction is inversely proportional to the wavelength. This means that as the wavelength increases, the index of refraction decreases, and vice versa. This relationship is described by Snell's Law.

4. Can the index of refraction change with different wavelengths?

Yes, the index of refraction can change with different wavelengths. This is because the speed of light in a medium can vary depending on the wavelength, resulting in a different index of refraction for each wavelength.

5. What factors can affect the accuracy of calculating the index of refraction with wavelength?

The accuracy of calculating the index of refraction with wavelength can be affected by factors such as the precision of the measurements, the purity of the medium, and the temperature and pressure of the medium. Additionally, the behavior of light in complex materials, such as those with multiple layers or varying densities, can also affect the accuracy of the calculation.

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