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Interference
Bragg's law
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 Example 1:
Interference by two slits :
Playing with the
parameters generating the interference by two slits should
have shown you:
 As you increase angle under which you observe the
interfering waves, the amplitude of the diffracted
wave oscillates. Every time that the value of
d*sin(alpha)/lambda is an integer number, the
amplitude is high. If d*sin(alpha)/lambda is
0.5, 1.5, 2.5 etc. the amplitude is zero.
 As you increase the distance between the slits, the
angle at which the amplitude vanishes for the
first time becomes smaller.
 As you increase the wave length, the angle at which
the amplitude vanishes for the first time becomes
larger. If the wave length is larger than
d*sin(90)/0.5 = 2*d, the amplitude never vanishes completely.
 The maximum amplitude that you can get is the sum of the
two individual amplitudes.
 Example 2:
Bragg's law:
 As you increase angle under which you observe the
interfering waves, the amplitude of the diffracted
wave oscillates. Contrary to the last example, the
formula is slightly different. Every time that the value of
2*d*sin(theta)/lambda is an integer number, the
amplitude is high. If 2*d*sin(theta)/lambda is
0.5, 1.5, 2.5 etc. the amplitude is zero. Note the
additional factor of 2. This relationship is the
well known Bragg's law.
 To visuallize the optical retardation, i.e. the
length of the extra stretch that the red wave travels,
count off the number of wave lengths between the
two diagonal black lines. This stretched is drawn as
a thicker red line. The two diagonal lines mark the
wave front. Before the first and after the second
wave front, the relative phase of the two waves
does not change.
 As you increase the distance between the slits, the
angle at which the amplitude vanishes for the
first time becomes smaller.
 As you increase the wave length, the angle at which
the amplitude vanishes for the first time becomes
larger. If the wave length is larger than
2*d*sin(90)/0.5 = 4*d, the amplitude never vanishes completely.
Even for lambda greater than 2*d we would never observe the
first oder Bragg reflection.
As a consequence, you cannot use very long wave lengths
for a diffraction experiment !
 The maximum amplitude that you can get is the sum of the
two individual amplitudes.
 The position of the atom on the upper layer does not
influence the interference at all! The length of the
extra stretch that the red wave travels does not
change as you move the atom within the upper plane.
