Diffraction patterns can be seen using various light sources but
are most easily observed using a laser. 

If we direct a laser beam towards a narrow aperture (say, 10^{4}m
wide or less) and observe the transmitted light on a screen a couple
of metres away, we find a central bright patch of light
(much wider than the aperture) and bright and dark fringes
on the sides. 



The diagram below represents such a diffraction pattern. 

The red patches show approximately what is seen on the screen. 

The curve above the patches is a graph of relative intensity of
light against position on the screen. 





Although we are referring to this as a diffraction pattern, it
should bring to mind interference effects (see Interference and
Interference Patterns) 



The next diagram shows the same situation but with an even
narrower aperture. 





Two changes are noticeable: the central maximum (the
bright patch in the middle) is wider and
the maximum intensity is lower. 

Neither of these changes is surprising, having seen diffraction
effects in, for example, water waves. 



However, we might ask; how do we obtain interference effects
when there is only one source of light (one aperture)? 



One way to consider the situation is to imagine the narrow
aperture (the slit, to save typing) to be made up of two slits
each half the width... ok, I know, sounds like a trick but just
accept it for now! 



Calculation of the Fringe Spacing for a Single Slit
Diffraction pattern 

We imagine secondary sources (see Huygens' principle) of light at points A, B
and C in the slit. 

Consider light leaving these points at angle,
θ to the normal line, as shown
below. 

The slit width is b and B is the midpoint. 



We will assume that the rays drawn here meet at p, a point on a
screen, a few metres away. 

As the slit width, b is very small compared with the distance to
the screen, we can consider the rays to be very nearly parallel. 



Suppose that θ is such that the
difference between Cp and Ap is equal to one wavelength of the
light (this is called the path difference). 

This means that the path difference for light from A and B to p
will be λ/2. 

Therefore the light from A and B will
interfere destructively on the screen. 

From the diagram it is clear that 



In practice, the angle θ is very
small, so we can write 



(see here for explanation)
where θ is in radians. 




Now consider the slit to be made up of pairs of point
sources, A and B, A’ and B’, etc, as shown here. 

Light from all these pairs of points will also
interfere destructively at point p. 

Therefore we will have a minimum intensity (a
dark fringe) of the diffraction pattern at an angle
θ to the normal.. 









If the distance between the slit and the screen is D, then the
width of the central maximum (central bright patch) of a single
slit diffraction pattern is given by 





The above reasoning should not be considered as an explanation
of the diffraction pattern. 

It does, however, give a method of predicting where the minima
(dark fringes) of the pattern will occur. 



Even if it's not really an explanation... these predictions agree
with experiment, and that's what counts! 



Double Slit Diffraction/Interference Pattern 

If we now consider sending light through two slits placed near
each other (for example as in the Young's famous
double slit experiment)
we obtain an intensity distribution as shown below. 



Here we are assuming that the distance between the slits is much
greater than their width. 



Note that the single slit diffraction pattern is still visible
in the "envelope" (shown by the broken line). 



The fringes due to the double slits are much closer together
than in the single slit case because the distance between the slits
is greater then their width. 
