Introduction:
This lab was designed to help students understand more about diffraction, as well as
teaching them about the wave theory of light, as well as teaching students about
phenomena with light, such as single slit, double slit, and other diffraction patterns.
Theory:
Section 1.1:
The idea of this section is that when you have light
coming out of a slit, it travels a distance that changes
with height from which it left the slit, as in the diagram
included, here the light at the top travels a distance that
is
longer by s sin(theta) where s is the distance vertically
between the bottom light ray and the light ray being
examined.
This separation of distances makes the light
out of phase with itself as by the equation Φ=(2πs(sin(θ))/λ.
The condition for a
maximum by this theory is b sin
α
= (k + ½)
λ,
where k is any integer, and the
minimums are given by the equation b sin
α
= k
λ.
This equation is actually inherently
flawed, while a maximum would be expected at 3pi (not at
pi, because of interference),
the actual maximum is at 8.94, so these equations are only accurate to within 5%.
Question: I was taught that when looking at the wave theory
of light and sound, you could consider the light to be similar
to that of a wave when you drop a rock into a pool of still
water.
The water will ripple outwards and the expansion
could be seen as a combination of the same type of pulses
that started the first wave, each occurring instantaneously
around the edge of the previous wave, as depicted in my
drawing to the right.
When the rays are not parallel, I
imagine that you would use this same model, but on a
slightly different axis, as in this drawing below the previous
one.
This also is demonstrated in my drawing below, showing
the equivalent in kind of a ray format where the rays shown are
the maximums.
This is to say that when you judge distances
you must
account for the
fact that there is
an inherent
angle to begin
with, so you
would need to measure theta from the axis
of the slit, not from the perpendicular to
which the ray had been traveling.