Fraunhofer diffraction - Single slit
spectrometer
Figure 1 (b)
telescope
Figure 1 (a)
adjustable slit
narrow slit
wide slit
The Fraunhofer diffraction due to a single slit is very easy to observe. An adjustable slit is
placed on the table of a spectroscope and a monochromatic light source is viewed through it
using the spectroscope telescope (see Figure 1(a)). An image of the slit is seen as shown in
Figure 1(b). As the slit is narrowed a broad diffraction pattern spreads out either side of the slit,
only disappearing when the width of the slit is equal to or less than one wavelength of the light
used.
The diffraction at a single slit of width a is shown in Figure 2.
Diffraction occurs in all directions to the right of the slit but
we will just concentrate on one direction towards a point P in
a direction  to the original direction of the waves. Plane
waves arrive at P due to diffraction at the slit AB. Waves
coming from the two sides of the slit have a path difference
BN and therefore interference results.
Figure 2
B
N
a

A
But BN = a sin , and if this is equal to the wavelength of
P
the light () the light from the top of the slit and the bottom of
the slit a will cancel out.and a minimum is observed at P.
This is because if the path difference between the two extremes of the slit is exactly one
wavelength there will be points in the upper and lower halves of the slit that will be half a
wavelength out of phase.
Therefore the general condition for a minimum for a single slit is:
Intensity
m = a sin 
Figure 3
where m = 1,2,3,4 and so on.
The path difference between light from the top and
bottom of the slit is written m where m is the number
of wavelengths ‘fitting into’ BN. m is also known as the
‘order’ of the diffraction image.
-
+
If the intensity distribution for a single slit is plotted against distance from the slit, a graph similar
to that shown that shown in Figure 3 will be obtained. The effect on the pattern of a change of
wavelength is shown in Figure 4.
1
Single slit diffraction
These two diagrams show the effect of a change of wavelength on the single slit diffraction
pattern. The pattern for red light is broader than that for blue because of the longer wavelength
of red light.
Intensity
Blue light – short wavelength
giving a narrow diffraction
pattern
-
Intensity
Figure 4
+
Angle of diffraction ()
Red light – long wavelength
giving a broad diffraction
pattern
-
+
Angle of diffraction ()
2