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SingleSlit Experiment
One should discuss the nature of the Fraunhofer diffraction
pattern produced by a single slit^{3}. Some important features of this problem can be
deduced by examining waves coming from various portions of the
slit, as shown in Figure 1a. According to Huygens´
principle, each portion of the slit acts as a source of waves.
Hence, light from one portion of the slit can interfere with light
from another portion, and the resultant intensity on the screen
will depend on the angle .
Figure 1:
Diffraction by single narrow
slit and its intensity distribution [3]

To analyze the diffraction pattern, it is convenient to divide the
slit in two halves, as in Figure 1a. All the waves that
originate from the slit are in phase. Consider waves 1 and 3,
which originate from the bottom and center of the slit,
respectively. Wave 1 travels farther than wave 3 by an amount
equal to the path difference
, where is the
width of the slit. Similarly, the path difference between waves 2
and 4 is also
. If this path difference is
exactly one half of a wavelength , the two waves
cancel each other and destructive interference results. This is
true, in fact, for any two waves that originate at points
separated by half the slit width because the phase difference
between two such points is . Therefore, waves from
the upper half of the slit interfere destructively with
waves from the lower half of the slit when

(7) 
or when

(8) 
If we divide the slit into four parts rather than two and use
similar reasoning, we find that the screen is also dark when

(9) 
Likewise, we can divide the slit into six parts and show that
darkness occurs on the screen when

(10) 
which can be simply understood from [3]
Therefore, the general condition for destructive
interference is

(11) 
Equation 11 gives the values of for which
the diffraction pattern has zero intensity, that is, where a dark
fringe is formed. However, it gives no information about the
variation in intensity along the screen. The general features of
the intensity distribution along the screen are shown in
Figure 1b. A broad central bright fringe is observed,
flanked by much weaker, alternating bright fringes. The various
dark fringes (point of zero intensity) occur at the values of
that satisfy Equation 11. The position of
the points of constructive interference lies approximately halfway
between the dark fringes. Note that the central bright fringe is
twice as wide as the weaker bright fringes. In this section was
referred to the alternating dark and bright bands on the screen as
a diffraction pattern, while in the case of Young´s doubleslit
experiment (see fig. 2) a similar pattern is referred to
Figure 2:
Young´s doubleslit
experiment [3]

an interference pattern. Also, there should be noted that the
derivation of the equations associated with interference and
diffraction effects are similar in the way that they consider the
addition of waves that are either in or out of phase. The effects
of interference and diffraction can be distinguished as follows.
When the waves to be added come from two or more openings
(sources), as in Young´s experiment, the resulting pattern is
called an interference pattern. When various portions of a single
wave interfere, as in this section, the result is a diffraction
pattern.
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