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The Diffraction Grating
A diffraction grating has thousands of narrow, parallel apertures (referred to as lines).  
A typical grating might have 500linesmm-1 or more.  
The behaviour of light passing through a diffraction grating can be analyzed in the same way as was used for Young’s two slit experiment.  
 
The rays represent the paths of light from 4 adjacent slits (lines) in the grating to a point on a screen.  
The screen will be a couple of metres away so, as d is of the order of 10-5m, we will assume that these rays are parallel.  
   
If the distance, b-c (the path difference for waves from slits a and b) is λ, then these waves will interfere constructively.  
Looking at the similar triangles, abc, ade, afg, etc we can say that, if b-c = λ then d-e = 2λ, f-g = 3λ and so on.  
In other words all these waves will interfere constructively at the point on the screen corresponding to the direction θ.  
We therefore see a well defined maximum of the diffraction pattern at this point, called a diffraction image (as it is an image of the source of light produced by the process of diffraction).  
   
Other maxima will occur when b–c = 2λ, 3λ etc.  
   
The width of the apertures here is much less than in Young’s experiment.  
This means that the angles at which the maxima of the pattern occur are not small angles.  
We therefore find the positions of the maxima of the diffraction pattern (equivalent to the bright fringes in Young's experiment) using  
 
where n (= 0, 1, 2 etc) is now called the order of the image (the central maximum being the zeroth order image).  
Gratings are usually marked with their number of lines mm-1, the distance d (in mm) is therefore simply the reciprocal of this number.  
See here for more detail of the derivation of the equation.  
   
In the above we have been assuming a monochromatic (single colour) source of light.  
If the grating is illuminated by white light then the positions of the images for different colours will occur at different places on the screen.  
This means that a diffraction grating can be used to produce a spectrum of the light source.  
   
The diagrams below show this idea.  
The numbers near the screen are the values of n, the order of the image.  
Note that the zeroth order image is still white because it corresponds to zero path difference between waves so all the colours have a maximum at the centre of the pattern (zero×λ is zero, whatever λ you choose!).  
 
View of the screen  
 
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