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The law of refraction, which is generally
known as Snell's law, governs the behaviour of lightrays as
they propagate across a sharp interface between two
transparent dielectric media.
Consider a lightray incident on a plane interface between two
transparent dielectric media, labelled 1 and 2, as shown in Fig. 57.
The law of refraction states that the incident ray, the refracted ray,
and the normal to the interface, all lie in the same plane.
Furthermore,

(341) 
where is the angle subtended between the incident ray and
the normal to the interface, and is the angle subtended between the
refracted ray and the normal to the
interface. The quantities and are
termed the refractive indices of media 1 and 2, respectively.
Thus, the law of refraction predicts that a lightray always
deviates more towards
the normal in the optically denser medium: i.e.,
the medium with the higher refractive index. Note that in the figure. The law of refraction also holds for nonplanar
interfaces, provided that the normal to the interface at any given point
is understood to be the normal to the local tangent plane of the
interface at that
point.
Figure 57:
The law of refraction.

By definition, the refractive index of a dielectric medium
of dielectric constant is given by

(342) 
Table 4 shows the refractive indices of some common
materials (for yellow light of wavelength nm).
Table 4:
Refractive indices of some common materials at nm.
Material 

Air (STP) 
1.00029 
Water 
1.33 
Ice 
1.31 
Glass: 

Light flint 
1.58 
Heavy flint 
1.65 
Heaviest flint 
1.89 
Diamond 
2.42 

The law of refraction follows directly from the fact that
the speed with which light propagates through a dielectric medium
is inversely proportional to the refractive index of the
medium (see Sect. 11.3). In fact,

(343) 
where is the speed of light in a vacuum. Consider two
parallel lightrays, and , incident at an angle with
respect to the normal to the interface between two dielectric media,
1 and 2. Let the refractive indices of the two media be and
respectively, with . It is clear from Fig. 58
that ray must move from point
to point , in medium 1, in the same time interval,
, in which
ray moves between points and , in medium 2. Now, the
speed of light in medium 1 is , whereas the speed
of light in medium 2 is . It follows that the
length is given by
, whereas the
length is given by
. By trigonometry,

(344) 
and

(345) 
Hence,

(346) 
which can be rearranged to give Snell's law. Note that the
lines and represent wavefronts in media 1 and 2, respectively, and,
therefore, cross rays and at rightangles.
Figure 58:
Derivation of Snell's law.

When light passes from one dielectric medium to another
its velocity changes, but its frequency remains unchanged.
Since, for all waves, where is the wavelength,
it follows that the wavelength of light must also change as it crosses
an interface between two different media.
Suppose that light propagates
from medium 1 to medium 2. Let and be the refractive
indices of the two media, respectively. The ratio of the
wavelengths in the two media is given by

(347) 
Thus, as light moves from air to glass its
wavelength decreases.
Next: Total Internal Reflection
Up: Geometric Optics
Previous: Law of Reflection
Richard Fitzpatrick
20070714