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Single Slit Diffraction

Submitted by mathhelp7
Mon, 28 Jan 2013

Introduction to single slit diffraction:

Diffraction: Light waves bending around the edge of obstacle, narrow opening or apertures and penetrate into the geometrical shadow region is diffraction. Light suffers some deviation from its straight path in passing close to the edges of obstacle. Light of wavelength either equal to or larger than slit width spreads out in all directions while passing through the slit. These waves diffract and produce a pattern on the screen. The pattern consists of light and dark areas which is similar to the interference pattern. The intensity of the band gradually decreases as we move the higher order of the diffraction pattern where the intensity is almost same for all bands in the interference pattern Light suffers some deviation from its straight path in passing close to the edges of obstacle. When light passes along edge of blade or a thin film, then lines of maxima and minima that run approximately parallel to the sharp edge are observed. It is found that diffraction produces bright and dark fringes corresponding to maxima and minima lines know as diffraction bands or fringes. This was initially observed and explained by Fresnel taking the concept of Huygens' Principle of wavelet in conjunction of interference. It should be remember that diffraction is observed only when a portion of the wave front is cut off by some edge.

Diffraction from Single Slit:

When a wave front of monochromatic light propagating normally to the slit is incident on it then the diffracted light moving along the shadow region is focused by means of lens on the screen. Every point of the wave front in the plane of the slit is source of secondary wave front traveling normally to the slit. Depending upon the path difference between the secondary wave fronts from the original wave front, the condition of maximum intensity (bright) and minimum intensity (dark) patterns are observed.

Condition of Single Slit Diffraction:

The two rays are parallel at an angle from the centre axis. The path difference between these rays is equal to the (a/2) sin θ Here 'a' is the width of the slit and theta is the angle made by the wave fronts with the central axis This path difference is equal to half the wavelength of the incident which is the condition for the dark fringe = λ / 2 The general equation for condition of minimum intensity or dark fringe higher order fringes is given as (a/2) sin θ = m ( λ / 2 ) sin θ = m ( λ / a ) Where m = 1,2,3,...... This is the equation for the dark fringe in diffraction pattern.


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