Snell’s Law

Theory and background

A number of great scientists independently discovered the law now bearing the name of Willebrord Snell. Among them were Descartes, Fermat and Harriot, all working in the 1600s. Preceding all of these by over 600 years was a scientist from Bagdad, Ibn Sahl, who first published it in 984. By rights we should call it Sahl’s Law, but the name Snell is now so established that it will likely never change. Its generic name is The Law of Refraction.

Snell’s law describes the way light bends or refracts when it passes from one material to another. It depends upon the angle of the incoming light, the angle of incidence, θ1, and the indices of refraction of the two materials, n1 and n2 . The most challenging part of learning to use this law is getting used to the way we define the angles of incidence and refraction. As shown in the diagram below, all angles are defined with respect to a normal line to the surface, not the surface itself.

This is a theme we’ve seen several time in physics and mathematics and it takes some time for it to seem like a good idea, but trust me, it is a good idea for higher physics and the mathematics associated with it.

Snell’s law can now be written mathematically as:

This allows one to predict how light will bend if you know the incident angle and the indices of refraction. Alternatively, if you can measure the angles of incidence and refraction it provides a way of measure refractive indices.

Procedure

For today’s lab we will be using two mediums; air (n = 1.0) and a clear plastic (n = 1.50). The shape of the piece of plastic is an equilateral prism. When set up properly, a light beam will be bent resulting in a scenario like this:

Briefly, we will experimentally measure the angles that the rays B and C make with the original direction of A and compare those angles with predictions from Snell’s Law assuming that the prism has an index of refraction of 1.50.

Detailed procedure

  1. Turn on the light source and select a single light beam.
  2. Using the blank template on the last page, align this beam (ray A) along the dotted line marked “Ray A” on the template. (The other, lighter dotted lines are for geometrical reference: they are parallel to A.) The template is rotated with respect to the diagram above to allow greater accuracy in drawing.)
  3. Place your prism in the proper location, making sure that its rear face lines up perfectly parallel with the bold line.
  4. Make sure that you see a ray pattern similar to that shown above. If not, see your instructor.
  5. Mark with a pencil or pen the locations where A and B meet and where B and C meet.
  6. Also mark a location on the ray C that is far away from the prism. Double-check to make sure that all of these dots line up with their proper locations (i.e. the prism or light source weren’t bumped during the drawing process.)
  7. Remove the prism and draw the rays between the points. This master copy can be used by all lab partners or additional trials can be made by various partners using fresh templates.
  8. Measure the angles that B and C make with the original direction of A. Try using a protractor first. (It is helpful to extend B beyond the prism area for measurement, even though the ray didn’t really go there.)
  9. Use trigonometry to re-measure the angles. Make sure you explain your trigonometric reasoning in your discussion. It is helpful to recopy the triangles on a separate sheet of paper as the template will get too crowded if you start to do calculations directly on it.

Comparison of angles; all with respect to the original direction of ray A.

Ray / protractor / trigonometry / Snell (theory)
B
C

Discussion Questions

  1. Carpenters and other craftsmen seldom use protractors to measure angles. Based upon your experiences above, comment on why that is probably a good idea.
  2. Fill in the last column of the table using Snell’s Law. Please show all your work, including diagrams. (Can attach as a separate handwritten sheet.)
  3. Compare your theoretical and experimental numbers. What is (are) a significant source(s) of error?
  4. Solve the following problem and include your solution as part of your lab report. (Again, may be handwritten and attached.)

A mirror is constructed of a sheet of plastic 5.0mm thick with a shiny metal coating on the back. If a laser beam comes in at an angle of 65 degrees with respect to the surface of the plastic and the plastic has an index of refraction of 1.63 (a) at what angle (with respect to the surface) does the light emerge back into the air after being reflected from the back surface? (b) how far apart are the locations of the entry point for the incident ray and the exit point for the reflected ray? It will help tremendously if you draw a good diagram.

D. Boucher 3/2013 (first version)


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