1. Snell’s Law

2. Snell's law
In optics and physics, Snell's law (also known as Descartes' law, the Snell–Descartes law, and the law of refraction) is a formula used to describe the relationship between the angle of incident and refraction when referring to light or other waves passing through a boundary between two different isotropic media, such as water and glass. The law says that the ratio of the sines of the angles of incidence and of refraction is a constant that depends on the media. The refractive index can be calculated by rearranging the formula accordingly.

3. Index of Refraction
The index of refraction of a material is defined by the speed of light in vacuum c divided by the speed of light through the material v. n = c/v

4. Snell’s Law qi qr air water
ni - index of incident qi – angle of incident
nr - index of refraction qr – angle of refraction

5. Index of refraction of common materials
Vacuum 1
Crown Glass
1.52
Air
1.003
Salt
1.54
Water
1.33
Asphalt
1.635
Ethyl Alcohol
1.36
Heavy Flint
Glass
1.65
Fused quartz
1.4585
Diamond
2.42
Whale oil
1.460
Lead
2.6

6. Example 1
Light travels from air into an optical fiber with an index of refraction of (a) In which direction does the light bend? (b) If the angle of incidence on the end of the fiber is 22o, what is the angle of refraction inside the fiber? (c) Sketch the path of light as it changes media.

7. Since the light is traveling from a rarer region (lower n) to a denser region (higher n), it will bend toward the normal.
We will identify air as medium 1 and the fiber as medium 2.  Thus, ni = 1.00, nr = 1.44, and θi = 22o.  Snell's Law then becomes

9. Example 2
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 30o, what is the angle of refraction outside the fiber? (b) How would your answer be different if the angle of incidence was 50o?

10. Since the light is now traveling from the fiber into air, we will call the fiber incident material and air refracted material. Thus, ni = 1.44, nr = 1.00, and θi = 30o. Snell's Law then becomes (1.44) sin 30o = 1.00 sin θr. sin θr = (1.44/1.00) sin 30o sin θr = 1.44 (0.500) sin θr = θr = sin-1 (0.720) = 46o

11. b. Replacing the angle of incidence with 50o gives sin θr = (1. 44/1
b. Replacing the angle of incidence with 50o gives sin θr = (1.44/1.00) sin 50o sin θr = 1.44 (0.766) = This equality cannot be met, so light cannot exit the fiber under these conditions.