Description:
A right equilateral triangular prism is used to show the critical angle of plastic, and how total internal reflection can be used to bend a beam of light 90° or 180° from it's original trajectory.
Watch Video:
Possible Incorporated Topics:
 Snell's Law
 Refraction
Theory:
Snell's law of reflection says that, for light passing from one medium (with index of refraction n_{1}) into another medium (index n_{2}) obeys the following relation: n_{1} sin(q_{1}) = n_{2} sin(q_{2}) where q_{1} is the angle of incidence and q_{2} is the angle of refraction. Rearranging this equation, we find q_{2} = sin^{1}[(n_{1}/n_{2})sinq_{1}] Now assume that n_{1} > n_{2} (this would be like having a beam of light in glass, n ~ 1.5 passing into air, n ~ 1, for example). We know that the argument of the inverse sine function must be between minus one and one. In this case, 1 ≤ (n_{1}/n_{2})sinq_{1} ≤ 1 ∴ sin(q_{1}) ≤ (n_{2}/n_{1}) where n_{2}/n_{1} is a fraction less than one. That is to say that there is a critical angle of incidence where q_{1} is given by sin(q_{1}) = n_{2}/n_{1}. At angles of incidence greater than this one, Snell's law no longer applies. 
Figure 1: Snell's Law at the boundary between two substances 
Experimentally, it is found that at angles greater than the critical angle, light is reflected back into the first medium. This effect is called total internal reflection, and can be demonstrated with a right equilateral triangular prism such as the one shown here (the sides are labelled for ease of referring to them later):
If a laser is shone into side A of the prism so that the light hits side C at a small angle of incidence, then most of the laser light is transmitted through side C and into the air around the prism.
Rotate the source of laser light clockwise about the prism to increase the incident angle of the light hitting side C. Eventually the angle of refraction will be 90°, and the refracted beam will be transmitted along the interface of the plastic and the air. Further increasing the angle of incidence will turn the beam totally inside the prism  this is total internal reflection.
Figure 3: Transmission through prism due to small incident angle 
Figure 4: Angles of incidence leading to total internal reflection 
90° Deviation of a Beam of Light:
A right equilateral triangular prism whose critical angle, q_{c}, is less than 45° can be used to deflect light at a right angle. Light shone normally on side A passes straight through, undeviated. Its angle of incidence on side C is 45°. This is greater than the critical angle, so the light is totally internally reflected. Since the angle of reflection is the same as the angle of incidence, the reflected ray moves off at 45° from side C's normal line. As you can see from the diagram to the right, the total deviation of the beam of light is 90°.
Figure 5: One case of Total Internal Reflection 
Figure 6: Real life demonstration of figure 5.

180° Deviation of a Beam of Light:
The same triangular prism as used before can be used to bend light 180°. Light enters normally on side C. Consequently, it is not refracted, and it travels straight through until it hits side B. Because of the inclination of side B, the ray hits it at an angle of 45°. The critical angle is less than 45°, so the ray hitting side B is totally internally reflected.
Continuing its travel, the ray is incident on side A at 45°, so it reflects as it did when it hit side B. Now deviated a full 180° from its original angle, the light continues on to hit side C again. Because the direction of the beam has simply been reversed, the light hits C normally again, and so is not refracted as it passes back into the air again.
Figure 7: Two cases of Total Internal Reflection 
Figure 8: Real life demonstration of figure 7

Apparatus:
 A right equilateral triangular prism
 A laser
 A small clear rod
Procedure:
Total Internal Reflection
 Place the right equilateral triangular prism on a flat surface.
 Shine the laser into side A of the prism such that the light is transmitted through side C.
 Rotate the source of laser light clockwise around the prism until no more light is transmitted through side C. All the light should be being reflected off side C and back into the prism. This is shown in the video below.
90° Deviation of a Beam of Light
 Point the laser normally on side A. The light should totally internally reflect off side C and back out side B. This deviates the light's path by 90°, as shown in the picture to the right.
180° Deviation of a Beam of Light:
 Shine the laser into side C so that it hits side A, reflects onto side B, then travels out side C again. The beam is thus deviated 180° from it's original path, as shown in the picture to the right.
SAFETY WARNINGS:
 Lasers can cause eye damage. Avoid exposure  never mount the laser at eyelevel or point it toward reflective surfaces no matter how careful you are.