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Diffraction Patterns
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, 10-4m 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 mid-point.  
 
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 C-p and A-p 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.  
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