phy1020.DVI

Chapter 46

Refraction

Light travels fastest (299,792,458 m/s) when it’s traveling through a vacuum. If light is traveling through
some other material, it slows down by a factor called theindex of refraction. The index of refractionnis a
dimensionless number defined by

nD

c

v

; (46.1)

wherecD299;792;458m/s is the speed of lightin vacuum, andvis the speed of lightin the medium. Since
vcalways, this meansn 1 ; typicallynis some number between 1 and 3, and will depend on the
medium.

46.1 Snell’s Law

If a light ray travels through some transparent medium and comes to an interface with another transparent
medium, the light ray will be bent as it moves into the new medium. This phenomenon is calledrefraction.
The ray will bendtowardthe normal if it moves into a medium of higher index of refraction, andawayfrom
the normal if it moves into a medium of lower index of refraction. The angle at which the ray is refracted is
given bySnell’s law, sometimes called thelaw of refraction:

n 1 sin 1 Dn 2 sin 2 (46.2)

Heren 1 andn 2 are the indices of refraction of the two media, and 1 and 2 are the angles of the incident
and refracted rays with respect to the normal.
In traveling from one medium to another, light will follow the path that takes theleast time; this idea is
calledFermat’s principle. Using the calculus, it is possible to derive Snell’s law from Fermat’s principle, and
thus show that Snell’s law gives the path light must follow in order to travel through the two media in the
least time.

46.2 Total Internal Reflection

It may sometimes happen that when light travels from a high-index medium to a low-index medium at a high
angle of incidence, that Snell’s law gives the sine of the angle of refraction to be greater than 1, so that the
angle of refraction is not defined. In this case, light is not refracted into the next medium at all; instead,
the light reflects off of the interface between the two media, and back into the higher-index medium. For
example, if a light ray in waternD1:33) is headed for an interface with air (nD1:00) at an angle of