Snell's law gives the relationship between angles of incidence and refraction for a wave impinging on an interface between two media with different indices of refraction. The law follows from the boundary condition that a wave be continuous across a boundary, which requires that the phase of the wave be constant on any given plane, resulting in

where and are the angles from the *normal* of the incident and refracted waves, respectively.

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 degree, what is the angle of
refraction inside the fiber?

Solution:

(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, n1 = 1.00, n2 = 1.44, and θ1 =
22o. Snell's Law then becomes

(1.00) sin 22 = 1.44 sin θ2.

sin θ2 = (1.00/1.44) sin 22 = 0.260

θ2 = sin-1 (0.260) =
15 degree.