## Monday, 6 June 2011

### Diffraction due to a narrow slit

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As light bends around an obstacle this phenomena can also be observe by passing light through a narrow slit which proves that light ray deviates from its straight path while passing from sharp edge.
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The figure below, shows the experimental arrangement for studying the diffraction of light due to a narrow slit.
 Fig    Diffraction due to a narrow slit AB

The slit AB width d is illuminated by a parallel beam of monochromatic light of wavelength λ. The screen s is placed parallel to the slit for observing the effects of the diffraction of light. A small portion of the incident wavefront passes through the narrow slit. Each point of this section of the wavefront sends out secondary wavelets to the screen. These wavelets then interfere to produce the diffraction pattern. It becomes simple to deal with rays instead of wavefronts as shown in the figure. In the above figure, only seven rays have been drawn whereas actually there are a large number of them. Let us consider rays 1 and 4 which are in phase when in the wavefront AB. After these reach the wavefront AC, ray 4 would have path difference ab say equal to λ/2. Thus, when these two rays reach point P on the screen they will interfere destructively. Similarly, each pair 2 and 6, 3 and 7 differ in path by λ/2 and will do the same. But the path difference ab = d/2 sinθ.
The equation for the first minimum is, then
$\frac{d}{2}\; sin\theta \: =\: \frac{\lambda }{2}$
$d\: sin\theta =\lambda$
In general, the condition for different orders of minima (dark regions) on either side of center are given by,
$d\: sin\theta =m\lambda$                  where m = 1,2,3,...

The region between any two consecutive minima both above and below O will be bright. A narrow slit, therefore, produces a series of bright and dark regions with the first bright region at the center of the pattern. Such a diffraction pattern is shown in figures given below:
 Diffraction due to monochromatic light                       Diffraction due to white light        t