Angle between two refraction angles

[goWlfpack]

Homework Statement

A certain kind of glass has an index of refraction of 1.640 for blue light of wavelength 440 nm and an index of 1.605 for red light of wavelength 670 nm. If a beam containing these two colors is incident at an angle of 30.0° on a piece of this glass, what is the angle between the two beams inside the glass?

Homework Equations

wavelength in vacuum/ waveleangth = n
(Sin theta)n - (sin theta2) n2

The Attempt at a Solution

I first tried to find the new index of refractice (n) for each wavemength in air. Then i used that to find each angle... then found the difference between them. any ideas where i went wrong?

 

[G01]

Why are you trying to find the indices of refraction for each color of light? They are given to you in the problem.

 

[physics girl phd]

Homework Statement

A certain kind of glass has an index of refraction of 1.640 for blue light of wavelength 440 nm and an index of 1.605 for red light of wavelength 670 nm. If a beam containing these two colors is incident at an angle of 30.0° on a piece of this glass, what is the angle between the two beams inside the glass?

Homework Equations

wavelength in vacuum/ waveleangth = n
(Sin theta)n - (sin theta2) n2

The Attempt at a Solution

I first tried to find the new index of refractice (n) for each wavemength in air. Then i used that to find each angle... then found the difference between them. any ideas where i went wrong?

I think you are making this too hard:
One difficulty with these types of problems is that they give you the wavelength of the two different colors (400nm and 600 nm). Generally, the wavelengths in a problem are always stated as vacuum (or air) wavelength (the difference here is negligible because the index of air is ~1). Due to dispersion (a different response from the material to the incoming E/M light wave of different frequency/color), the speed of light propagation in a material can depend on its frequency/color. This is represented by different indices of refraction for the different colors. This causes the light to spread out in colors when it enters a dispersive material (like glasses)... because the different indices cause different angles of refraction.

Because at this point you don't care about the wavelength in the material, only the angle, your second equation suffices:

(Sin theta)n - (sin theta2) n2
(It's called "Snell's law".. and note, there's no wavelength in this equation at all!)

Here theta would be the angle at which the light strikes the glass (relative to the normal), n would be the index of refraction of air. theta 2 is the angle relative to the normal of the refracted beam inside the glass, and n would be the index of refraction for that color. You should know all but theta2, the internal angle for each beam. Once you find the internal angles for each beam, you can find the angle between them (as you indicated).

Also check you intermediate answers: Which beam will be refracted more: Blue are red? Do your answers correspond?

If things look funny, make sure you have your calculator set on "degrees," or that you've converted your angle correctly. It's easy to forget this.