Angle between colors - dispersion

[BDR]

(a) A narrow beam of light containing yellow (660nm) and green (550nm) wavelengths goes from polystyrene to air, striking the surface at a 30 degree incident angle. What is the angle between the colors when they emerge? (b) How far would they have to travel to be separated by 1.00 mm?

I need some guidance on if i am working the problem right! Do i use Snell's Law?

1.49sin30 = 1.000293sin(angle)?

 

[Doc Al]

Yes, use Snell's law of refraction. But you need to know the refractive index for each wavelength. The angle of incidence is the same (30 degrees), but the angle of refraction will be slightly different for each wavelength.

 

[BDR]

Here is what I'm doing!

Yellow: 1.492sin(30) = 1.000293sinθ

Green: 1.493sin(30) = 1.000293sinθ

When I do the calculations i am not getting the correct. The answer is suppose to be 0.043 degrees and 1.33 m. Where do you think I am messing up the calculations?

 

[Doc Al]

Beats me since you didn't show your calculations!

Using those same equations I get 0.043 degrees, so I'm not sure where you went wrong. Try this: (1) Solve for the angle of refraction for each color; (2) Subtract those angles to find the angle between the two refracted colors.