Snell’s Law
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.
ni sin i  nr sin  r
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
Snell’s Law
air
ni sin  i  nr sin  r
i
water
r
ni - index of incident
nr - index of refraction
i – angle of incident
r – angle of refraction
Index of refraction of common materials
Material
n
Material
n
Vacuum
1
Crown Glass
1.52
Air
1.003
Salt
1.54
Water
1.33
Asphalt
1.635
Ethyl Alcohol
1.36
1.65
Fused quartz
1.4585
Heavy Flint
Glass
Diamond
Whale oil
1.460
Lead
2.6
2.42
Example 1
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 22o, 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, ni = 1.00, nr = 1.44, and
θi = 22o. Snell's Law then becomes
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?
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 = 0.720
θr = sin-1 (0.720) = 46o
b. Replacing the angle of incidence with 50o gives
sin θr = (1.44/1.00) sin 50o
sin θr = 1.44 (0.766) = 1.103
This equality cannot be met, so light cannot exit
the fiber under these conditions.