How Does Wavelength Affect Refraction Angle in Diamonds?

[asd1249jf]

Refraction problem!

Homework Statement

A beam of white light is incident on the surface of a diamond at an angle Theta_a. Since the index of refraction depends on the light's wavelength, the different colors that comprise white light will spread out as they pass through the diamond. For example, the indices of refraction in diamond are nred = 2.410 for red light and nblue = 2.450 for blue light. Thus, blue light and red light are refracted at different angles inside the diamond, as shown in the picture. The surrounding air has nair = 1.
http://img212.imageshack.us/img212/8778/problemyh8.jpg

A diamond is cut such that the angle between its top surface and its bottom surface is alpha. For alpha = 45 degrees, find the largest possible value of the incident angle theta_a such that the blue light is totally internally reflected off the bottom surface.

Homework Equations

Snells law
n1sin(theta_1) = n1sin(theta_2)

The Attempt at a Solution

I'm sorry, I couldn't even touch the problem. Can anyone give me like the slightest hints to this? I'm thinking it's related to finding the critical angle then applying it somehow, which turned out to be 24.09 degrees, but I'm completely stuck here.

 

[asd1249jf]

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[asd1249jf]

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[asd1249jf]

bumppppppppppppppppppppppppppp

 

[grant9076]

I can't stick around long but you can solve it by working backwards. You can use Snell's law to find the minimum incedence angle to reflect off the second bottom surface (left). You then use that to find the reflected angle off the first bottom surface (right) which is equal to the incedence angle at the first bottom surface (right). With that you can use goemetry to solve for the refracted angle through the top surface. You then use Snell's law to find the original incedence angle. Be advised, I have not done any physics in a very long time so someone else may be better able to help you.

 

[Fried Chicken]

It's not that bad. You should already know the critical angle,
sin(theta(crit)) = n(diamond)/n(air)
so sin^-1(theta) = sin^-1(n(diamond)/n(air))
so sin^-1(2.45/1) = 24.09°

Now for the second problem,
you know the critical angle, but b/c there is the 24° angle, you need to get the angle that it has in the diamond when it strikes the diamond, so you do
45° - 24.09 ° = 20.9°

Once you know that, you apply snells law.
n(air)sin(theta(a)) = n(diamond)sin(theta(diamond)
or
1sin(theta(air) = 2.45sin(theta(diamond)
so to find the angle of the air,
sin-1(2.45sin(theta(diamond))) = answer
sin-1(2.45*sin(20.9)) = 60.97°

Merry Christmas.

 

[Redbelly98]

Welcome to Physics Forums.

Please note for the future, it is against our policy to provide complete solutions and answers to homework problems.

Since the question was asked 2 years ago, it is not a big deal this time.