Snell’s Law (AND THEN SOME)
Anthony Osinski
Physics Teacher
Campbell High School
Prerequisites: Class will have already discussed the basics of waves (i.e. what happens to them at a boundary) and will have played with spring or rope translational waves on the floor to view effects. The law of reflection for waves will have already been discussed. Additionally, students will know that a light ray is only a visual representation of a series of wavefronts. IB students will have discussed this further in derivations of law of reflection via Huygen’s Principle.
Inquiry: Students will be given a large block of lucite and a ray box. Using these tools students are first to observe and then to quantitatively measure light “rays” as they impinge on the block. Protractors are readily available in the room. Students are also to draw the situations (or use some other representation – pipe cleaners???). May be helpful to block all but one of the slits in the ray box.
• Since the concept of the normal has already been introduced in discussing reflection, make sure students use this measurement as they measure and draw
• While doing the experiment, students are obviously going to see that the light ray bends – so we should give it a name now - REFRACTION
• Make sure that students are moving both the ray box and the block of lucite relative to each other – but preferably not at the same time (keeping one variable constant)
• If students do not pick up on the fact that some of the light is being reflected (conveniently place hand in direction of reflected light and as where it came from
• Students will probably want to talk about the light EXITING the lucite. Tell them to mentally note this. After
Snell’s Law is found, we will go back to this.
• Some sort of data table needs to be generated. The more values the better
Results: Hopefully a data table of two sets of angles, incident and refracted, will be generated. Problem is that
Snell’s Law does not just pop out of this data. So after some examination, trying to find a relationship, may have to suggest trigonometric functions of the angles. Eventually if we can work to the ratio of the sines of the angles we should come to a constant.
Graphing the sine of the incident angle vs, the sine of the refracted angle will give the index of refraction, which we can now name.
Rewrite sin( Θ incident)/sin ( Θ refracted) = n as more commonly seen equation
We can now proceed to work some sample problems :

Light travels from air into an optical fiber with an index of refraction of 1.44.
(a) In which direction does the light bend? (b) If the angle of incidence on the end of the fiber is 22 o , what is the angle of refraction inside the fiber? (c)
Sketch the path of light as it changes media.
(a) Since the light is traveling from a rarer region (lower n ) to a denser region
(higher n ), it will bend toward the normal .
(b) We will identify air as medium 1 and the fiber as medium 2. Thus, n
1
=
1.00, n
2
= 1.44, and θ
1
= 22 o . Snell's Law then becomes
(1.00) sin 22 o sin θ
2
= 1.44 sin θ
2
.
= (1.00/1.44) sin 22 o = 0.260
θ
2
= sin -1 (0.260) = 15 o .
(c) The path of the light is shown in the figure below.
Light traveling through an optical fiber (n=1.44) reaches the end of the fiber and exits into air. (a) If the angle of incidence on the end of the fiber is 30 o , what is the angle of refraction outside the fiber? (b) How would your answer be different if the angle of incidence were 50 o ?
(a) Since the light is now traveling from the fiber into air, we will call the fiber material 1 and air material 2. Thus, n
1
= 1.44, n
2
= 1.00, and θ
1
= 30 o .
Snell's Law then becomes

(1.44) sin 30 o = 1.00 sin θ
2
.
sin θ
2
= (1.44/1.00) sin 30 o = 1.44 (0.500) = 0.720
θ
2
= sin -1 (0.720) = 46 o .
Notice that this time, the angle of refraction is larger than the angle of incidence. The light is bending away from the normal as it enters a rarer material.
(b) Replacing the angle of incidence with 50 o gives sin θ
2
= (1.44/1.00) sin 50 o = 1.44 (0.766) = 1.103
This equality cannot be met, so light cannot exit the fiber under these conditions.
The situation in part (b) is an example of total internal reflection, discussed on the next content page.
Students need to remember that the sine of an angle cannot exceed 1.0, so we will acknowledge that something screwy is going on and see if it comes up later.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Since students have already noted that the light coming OUT of the lucite also bends, we will look at this as a class for time’s sake. Again using the lucite block and the ray box, vary angles of incidence. The first thing we can pull out of this is the index of refraction for air (now that we know the index for lucite). This now can be integrated into the simplified version of the formula above to give
N1 sin Θ 1 = N2sin Θ 2
Also need to discuss bending away from the normal vs towards the normal at this point
We can now examine problems and situations where air is not one of the mediums of transmission..
Check out Java Applet on : http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/refractionsnells.htm
Text for sample problems.
Total Internal reflection
At some point students will notice that the incident light ray from the lucite will no longer transmit through to the air. Why is this? Give the students some time to work on the formula – again replacing the indices of refraction we have already found. It may be stretch for them to find that at a certain angle in you will exceed 90 degrees

for the angle out. So at this point will introduce the concept of the critical angle. We can derive the formula below after it is realized that the angle of refraction cannot exceed 90 degrees and AT 90 degrees it is 1.00
Sin (critical angle) = ratio of indices of refraction
WHY does this happen only when going from lucite to air???? Generalize this as any situation where the light travels from a more dense to less dense medium.
Again, using the above applet, this can be demonstrated for any number of substances.
Uses
Fiber-optics. In addtion to research project demonstration, also have on hand coil of fiber-optic line and various toys using fiber-optics (Christmas tree??). Also need laser and plastic bottle with small hole in side of bottom.
Using this first fill bottle with water and let stream come out of the hole. Line up the laser and shine thru the bottle to the hole. The light will be carried with the water.
+Fiber-optics: Use a guide of glass or polymer to transmit the light
+Can transmit information via light signal as opposed to electrical signal
+Many wavelengths can be sent on the same cable
+Different detectors (photo-electric effect) pick up different signals
+ 10 Gigabytes of information per second can be sent on optics lines
+Possible future use is optic signal transmission INSIDE the computer – a miniaturized version of a macro optic grid
(Laser discussion to follow)
Websites: http://www.physicsclassroom.com/Class/refrn/refrntoc.html
Has a great discussion, diagrams, and a couple of sample problems
Snell song at : http://www.haverford.edu/physics-astro/songs/snell.htm
Another quickie Applet at: http://webphysics.davidson.edu/applets/Optics/fiber_optics.html
Shows a beam of light from outside fiber optic and then can be dragged inside.