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SteveM-
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Homework Statement
white light propagating in air is incident at 45 degrees on an equilateral prism Find the angular dispersion "gamma" of the outgoing beam if the prism has refractive indices n(red) = 1.582 and n(violet) = 1.633.
NOTE: "gamma" is just a variable for describing the angular dispersion.
Homework Equations
Snell's law n1sin(theta)=n2sin(theta)
adjusted for our purposes I came up with:
For incoming wight light:
n(air)sin(45) = n(red)*sin(theta(r1)) and n(air)sin(45) = n(violet)sin(theta(v))
solving these equations we can find our angles and use those to determine our outgoing theta for each wave:
n(red)sin(theta(r1)) = n(air)sin(theta(r2)) and
n(violet)sin(theta(v1))=n(air)sin(theta(v2))
The Attempt at a Solution
Well this seems like a simple plug and chuck, but the approach seems like it may be oversimplified, I think there may be some geometry somewhere that needs to be added, (i.e. should I add 45 degrees to the theta(r1) and use that degree value for the "theta(r1)" for the outgoing red beam angle?
Assuming I find the output angles then all I would need to do is take the difference of those angles to determine the angular dispersion "gamma"?
The given text available provides about half a paragraph talking about angular dispersion for the entire chapter on reflection and refraction, so if you guy's happen to know of any useful links I could refer to for FYI purposes, that would be appreciated as well, but in the mean time am I doing this correctly?
When I solved the numbers I basically got output angles of red and violate that were suspiciously close making the difference near zero... the only thing that seems correct is that my angle for red is above the angle for violate which is expected...