How Does Snell's Law Affect Wavelength?

[diggadigga]

Homework Statement

With 2019 behind him, Rohan refracted on the past year by wearing his 2020-Hindsight- Fiber-Optic Glasses to view the magic coherent 2019 Crystal Ball. Unbeknownst to Rohan, the 2020 Glasses were defective because the left and right fibers of the glasses had different indices. Fiber Optic 1 had an index of refraction n1 = 1.5 and Fiber Optic 2 had index n2 = 2.5. Both fiber optic paths are exactly 339 cm in length. Bright white light, emitted by the very distant Magic Crystal Ball, enters each fiber of the glasses and travels along their radii until their images are superimposed on the single Screen of the glasses. What’s the most prominent color that Rohan sees in the image? Assume the fibers are very thin. Hint: 1 nm = 1×10-9 m.

(a) Red ( ≃ 647 nm)
(b) Yellow ( ≃ 575 nm)
(c) Green ( ≃ 516 nm)
(d) Blue ( ≃ 452 nm)
(e) White (all wavelengths)

Relevant Equations

There aren’t any relevant equations on the test

I thought about using the snell’s law because it involves different refractive index but I have no idea why the wavelength would be affected by the snell’s law. I thought that maybe if I found the frequency I might be able to get the wavelength but, I don’t know which formula I should use. I then tried to use the dispersion crystal, but I don’t know why I would do that.

 

[berkeman]

Welcome to PF.

to view the magic coherent 2019 Crystal Ball.

Bright white light, emitted by the very distant Magic Crystal Ball, enters each fiber of the glasses and travels along their radii until their images are superimposed on the single Screen of the glasses.

Pretty goofy question. Can you say more about the apparent problem issue between the two parts of the problem statement that I've highlighted?

 

[diggadigga]

the magic coherent thing isn't related to the problem, the crystal just emits white light this image from the problem might help http://ibb.co/QC2LCym

 

[haruspex]

the magic coherent thing isn't related to the problem

It is a strange problem, but it seems to me coherence is key.
I think you have to assume that for each wavelength emitted by the crystal ball it is emitted coherently; that is, the waves of a given wavelength enter the fibres in phase.

 

[diggadigga]

From my understanding white light is made from all of the visible light's wavelength, and since their wavelength is different they would never be coherent, is there a formula that you could give that would better explain this?

 

[haruspex]

From my understanding white light is made from all of the visible light's wavelength, and since their wavelength is different they would never be coherent, is there a formula that you could give that would better explain this?

That's why I say it's a bit strange.
Note that they give you wavelengths of four specific colours, so assume this white light is made of just those four.
(And yes, it is possible to blend three or more pure wavelengths so that a human could not distinguish from white light as a continuous spectrum, so "white" does not imply a continuous spectrum.)
Each colour could in itself be coherent, and on that basis you can answer the problem.