Snell's Law tells us how light bends when it moves out
of one medium and into another. In particular, it tells us how a
ray of light in air bends as it enters a glass lens.
Figure 1 
Light Entering Glass:

Whenever light passes from one medium to another with a different
refractive index, its path bends. If the
refractive index of the
medium it's leaving is N
_{0} and that of the medium it's
entering is N
_{1}, and if the angle from perpendicular with
which it hits the interface is θ
_{0} and that which it enters
the new medium is θ
_{1}, then Snell's Law says that
1) 
On the remainder of this page we'll present a simple derivation
of this law.
Change in Wavelength with Velocity
Frequency can't vary as radiation passes through an interface  the
same number of wave crests must "come out" as "went in". So,
since velocity divided by frequency is wavelength, the wavelength must
change at the interface. If we use λ for wavelength, ν for
frequency,
N for refractive index, and
V for the
velocity of light in the medium, then within a single medium we have:
2)
And at the interface between two media we have:
3)
Bending of the Waves At the Interface
We will now
assume that a beam of light travels as a sequence
of parallel, flat wave crests, and that the direction of travel is
always
perpendicular
to each wave crest. The distance between the crests is the
wavelength, and it changes as the beam enters a new medium, as a result
of which each crest must
bend at the interface. Using
this assumption, and looking at
figure 2, we
can determine how much the wave crests must bend, and consequently how
much the beam's direction must change.
Figure 2  Snell's
Law:

The segment labeled "
r" in figure 2 is the hypotenuse of
two right triangles in the diagram, labeled
T_{0}
and
T_{1}. The
red side of
triangle
T_{0} has length λ
_{0}, and the
red side of triangle
T_{1} has length λ
_{1}.
Since they're right triangles, we can see that
4)
Dividing the first of these into the second, we have
5)
Plugging equation (3) into equation (5) we obtain the result we wanted,
which is
6)
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created on 1/4/2009