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1. Homework Statement
The two rays shown below, a and b, have different wavelengths. They travel through the glass prism as shown; 1) is this possible? 2) If this is possible, which has the longer wavelength, ray a or ray b?
[see attached figure]
2. Homework Equations
λ = λi/n
critical angle = arcsin(n2/n1)
3. The Attempt at a Solution
We are trying to think through this but we keep hitting mental blocks. We know that a and b have different wavelengths, and that both of the wavelengths will change by the same factor when they enter the glass. We also know that you will get total internal reflection (TIR) at some angle specified by the indices of refraction for the glass prism and air.
We aren't totally convinced that this is possible, because the critical angle depends wholly on the indices of refraction, which are independent of wavelength. Is this correct reasoning? By this logic, it is not possible.
Thank you so much!
The two rays shown below, a and b, have different wavelengths. They travel through the glass prism as shown; 1) is this possible? 2) If this is possible, which has the longer wavelength, ray a or ray b?
[see attached figure]
2. Homework Equations
λ = λi/n
critical angle = arcsin(n2/n1)
3. The Attempt at a Solution
We are trying to think through this but we keep hitting mental blocks. We know that a and b have different wavelengths, and that both of the wavelengths will change by the same factor when they enter the glass. We also know that you will get total internal reflection (TIR) at some angle specified by the indices of refraction for the glass prism and air.
We aren't totally convinced that this is possible, because the critical angle depends wholly on the indices of refraction, which are independent of wavelength. Is this correct reasoning? By this logic, it is not possible.
Thank you so much!
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