internal reflection?

Question

Hey everyone someone please help. I asked my professor about this in class and he didnt listen to me just interupted so i still dont know. here it is
2 transparent materials having indexes of refraction 1.27 and 1.31 are placed in to contact. Is it possible for total internal reflection to occur at the boundry between the two materials? In either case, be specific about details or constrants.

Some one help all i know is it has something to do with n1 (v1)=n2(v2) or something like that.

Answer 1

Forget about the v's: those are velocities, and you're really interested in angles here.

Use Snell's law:

n1/n2 = sin(θ_2) / sin(θ_1)

Or, plugging in your numbers:

1.27 / 1.31 = sin(θ_2) / sin(θ_1) = 0.969

Total internal reflection occurs when the angle of the low-index substace goes to 90 degrees (that is, when sin(θ_1) = 1). So:

sin(θ_2) / 1 = 0.969
sin(θ_2) = 0.969

Which means θ_2 = 75.8 degrees.

So the answer is "yes." The critical angle is 75.8 degrees.

Answer 2

Please note that some of the information on this page does not appear because I wasn't able to copy it. Use the URL at the bottom to see the complete copy.

Optical description

Total internal reflectionTotal internal reflection can be demonstrated using a semi-circular glass block. A "ray box" shines a narrow beam of light (a "ray") onto the glass. The semi-circular shape ensures that a ray pointing towards the center of the flat face will hit the surface at right angles by preventing refraction at the air/glass boundary. At the glass/air boundary what happens will depend on the angle. Where θc is the critical angle:

If θ < θc, as with the red ray in the above figure, the ray will split. Some of the ray will reflect off the boundary, and some will refract as it passes through.
If θ > θc, as with the blue ray, all of the ray reflects from the boundary. None passes through.
The second situation is total internal reflection.

This physical property makes optical fibres useful, and rainbows and prismatic binoculars possible. It is also what gives diamonds their distinctive sparkle, as diamond has an extremely high refractive index.

An important side effect of total internal reflection is the propagation of an evanescent wave across the boundary surface. This wave may lead to a phenomenon known as frustrated total internal reflection.


[edit] Critical angle
The critical angle is the angle of incidence above which total internal reflection occurs. The angle of incidence is measured with respect to the normal at the refractive boundary. The critical angle θc is given by:


where n2 is the refractive index of the less dense medium, and n1 is the refractive index of the denser medium. This equation is a simple application of Snell's law where the angle of refraction is 90°.

If the incident ray is precisely at the critical angle, the refracted ray is tangent to the boundary at the point of incidence. For visible light travelling from glass into air (or vacuum), the critical angle is approximately 41.8°. The critical angle for diamond is about 24.4°, which means that light is much more likely to be internally reflected within a diamond. Diamonds for jewelry are cut to take advantage of this; in particular the brilliant cut is designed to achieve high total reflection of light entering the diamond, and high dispersion of the reflected light (known to jewelers as fire).

If the fraction: is greater than 1, then arcsin is not defined--meaning that total internal reflection does not occur even at very shallow or grazing incident angles. So the critical angle is only defined for .

http://en.wikipedia.org/wiki/Total_internal_reflection