Find index of refraction of the prism for 2 wavelengths

[Ed Boon]

Homework Statement

Homework Equations

Snell's Law: na*sin(theta of a) = nb*sin(theta of b)
wavelength = index of refraction / n
n = c / v

The Attempt at a Solution

The only information given in the problem is the 2 angles of refraction and of course n of air is 1, I do not understand how to get the index of refraction for both wavelengths with just the angles given and nothing more. They do not state the wavelengths of the rays. I assume it is solvable because it is in the text but if someone could maybe lead me in any direction I would appreciate it.
Thanks

 

[mgb_phys]

It's not asking for their wavelengths, you just have to assume the wavelengths are different so that the refractive index can be different.
It's simply a geometry question, find the angle from the normal for each of the exit rays and then just use Snell's law to calculate 'n' for each of them.

 

[Ed Boon]

It's not asking for their wavelengths, you just have to assume the wavelengths are different so that the refractive index can be different.
It's simply a geometry question, find the angle from the normal for each of the exit rays and then just use Snell's law to calculate 'n' for each of them.

Thats what I was thinking so you will have na*sin(theta of a) equals to both nb*sin(0b) and nc*sin(0c) (b and c the 2 refractions) so if u set the 2 equal to each other:
nb*sin(20.5) = nc*sin(12)
dont you need more info to get the exact values instead of just a ratio?
thanks for the quick response

 

[mgb_phys]

Assuming the prism is in air, anf consideringthe refraction at the exit face - isn't it just
na sin(internal angle ) = 1 * sin(12+external angle)
nb sin(internal angle ) = 1 * sin(12+8.5+external angle)

And the angle from normal inside the prism is just the angle from normal to the horizontal dashed line outside ( and is equal to the prism wedge angle)
na sin(x) = sin (12 + x)
nb sin(x) = sin(20.5 + x)
It should be possible to rearrange this to get exact values of na and nb without knowingx