Multiple wavelengths and angles of refraction?

Question

I have three wavelengths, 400 nm, 500 nm, and 650 nm.  I need to prove that the angles of refraction vary with wavelength when they go from air through a block of crown glass.  

What I tried doing was solving for a relative incidence of refraction for each wavelength by taking n=589/400, etc. and then plugging that into Snell's Law for each but I'm still not getting the right answer.  

Am I on the right track?

? · Accepted Answer

yes, flip it.

? · Answer

kind of.

so, you know Snell's law:
n1 sin(theta1) = n2 sin(theta2).
then
sin(theta2) = n1/n2 * sin(theta1);

since n2 will change for each wavelength then sin(theta2) will also change, meaning theta2 will change too!!!

more precisely:
for medium 1, n1=air, sin(theta1) = some number 
[some number, based on the angle value you choose; say 30 degrees, then sin(theta1)=0.5]

now, you have 3 wavelengths, so n2 (for the crown glass) will vary for each wavelength, correct?
you need to find out n2 for each wavelength.

take those values and plug them in 
sin(theta2) = n1/n2 * sin(theta1);
and that will give you each theta2 for each wavelength. you will see they are all different!

:-)

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Multiple wavelengths and angles of refraction?

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