Total Internal Reflection (TIR) using a Soda Bottle

Figure 1: Total Internal Reflection (TIR) causes light to bend through a stream of water.

 

Figure 2: A laser is pointed at a soda pop bottle with a hole at the bottom. Total internal reflection (TIR) is produced in a stream of water due to the water and light barrier.

The Video Explanation

Explanation

When light crosses into a new medium, some of the light will refract (bend) and some of it will reflect. The angle of refraction is given by Snell's Law:

Where n is the index of refrection, a property unique to each material. This, and the reflection, is shown in the following diagram.

Figure 4: Light refracts and reflects at the barrier between air and water.

Where θ1 is the angle of incidence, or the angle of the source of light, θr is the angle of reflection, and θ2 is the angle of refraction. However, Snell's Law will result in error when n1 is greater than n2. This is called a critical angle, and it is the minimum angle at which all light is reflected. The critical angle can be defined by:

This is the limiting case. If n1 ≥ n2, then θ2 = 90°.

Figure 5: At the critical angle, light travels through the plane where the two media meet.
In this case, nair = 1.00 nwater = 1.33. Therefore:

In this demo light will continually reflect through the stream of water creating total internal reflection (TIR). The stream of water will 'carry' the light though, to the end of the stream.

Figure 6: Total Internal Reflection (TIR) causes light to bend through a stream of water.

Total Internal Reflection is the principle behind fiber optics.

Figure 7: Total Internal Reflection is used to carry light in fiber optics.

For more information see Wikipedia's entry on Fiber Optics. http://en.wikipedia.org/wiki/Optical_fiber.

   Materials

• empty soda pop bottle (2 liter)
• tape
• hand drill
• drill bits
• water
• green laser
• bucket
• old books, etc for stands

Procedure

1. First set up the soda bottle by drilling a hole near the bottom of the bottle. Begin with a drill bit that has a diameter which is slightly larger than the diameter of the laser that will be used. We used a 1/4 inch drill bit, however sizes as small as 7/32 inch worked as well. 
2. First tape the hole and then fill the bottle with water. The cap will prevent leaking because it creates a vacuum in the bottle. 
3. Stand the soda bottle on top of a stack of books so the hole is facing the bucket. The laser should be placed in a binder clip so it stays on, and then set on a stack of books and papers. The laser should be lined up so that the laser light goes through the soda bottle, and into the center of the hole. See Figure 2 (top left picture) for details. 
4. Carefully remove the tape and then unscrew the top of the soda bottle. The light should reflect within the stream of water so that you could see at least a few points of reflection. The light should be visible through the entire stream. 
5. If the reflections of the light isn't clear, it may be necessary to expand the hole by drilling through the existing hole with a larger drill bit. This process may need to be repeated several times.

    Notes

• This is an messy experiment. Be ready to adjust the bucket which catches the stream of water. 
• Also be aware that the stream's curvature will change as the water level decreases. It will bend closer to the bottle, and the bucket may need to be adjusted again. When the water level is a little above the hole there will be no total internal reflection although the stream will continue. Place the cap back on, or put the bottle inside of the bucket. 
• Make sure to have lots of paper towels! Towels or rags could be useful too. However, this mess is water, and therefore easy to clean up. 
• Some resources suggest putting a drop of food coloring in the bottom of the bucket to match the laser light, giving the appearance that the water has permanently 'trapped' the colored light. This is a magic trick, and may cause students to misunderstand what total internal reflection is.

  References

http://wildcat.phys.northwestern.edu/vpl/optics/snell.htmlThis site contains an applet which allows the user to change the angles and indices of refraction. It is a more simple and straight version compared to Stony Brook's (the link below).
http://www.eserc.stonybrook.edu/ProjectJava/snell/This site is an applet which allows the user to change the angles and indices of refraction in order to observe reflection and refraction. There is a 'simpler version' option.
http://en.wikipedia.org/wiki/Total_internal_reflection
The Wikipedia entry on Total Internal Reflection
http://hyperphysics.phy-astr.gsu.edu/Hbase/phyopt/totint.html
An explanation of total internal reflection with drawings. It includes a calculator which determines the critical angle when the indices of reflection are provided.
http://www.glenbrook.k12.il.us/gbssci/phys/CLass/refrn/u14l3b.html
This is a tutorial on Total Internal Reflection with many drawings to explain the concepts.