# Interference and Diffraction

THEORY OF INTERFERENCE AND DIFFRACTION

CONSTRUCTIVE INTERFERENCE

At a point of maximum intensity, the path difference between the two waves must be an integral multiple of the wave length of light used .

DESTRUCTIVE INTERFERENCE

At a point of minimum intensity, the path difference between the two waves must be an odd multiple of half wave length of light used .

FRINGE WIDTH: Distance between two consecutive dark fringes is equal to the width of a bright fringe.

Similarly, distance between two consecutive bright fringes is equal to the width of a dark fringe.

DIFFRACTION OF LIGHT AT A SINGLE SLIT

i) the width of central maximum is twice that of a secondary maximum

ii) the intensity of the secondary maxima goes on decreasing with the order of maxima.

CENTRAL MAXIMUM: According to Huygens principle, when light falls on the slit, it becomes a source of secondary wavelets. These wavelets are initially in phase and spread out in all directions. Let C be the center of the slit AB. The rays travelling in a direction parallel to CO are brought to a focus at O. These rays meet at O in phase because they are initially in phase and their optical paths are also equal. Hence the wavelets reinforce each other producing a maximum at O.

Differences between INTERFERENCE and DIFFRACTION

1) Interference is due to interaction of light from two separate wave fronts originating from two coherent sources whereas diffraction is due to interaction of light from different parts of the same wave front.

2) In interference, the width of all fringes are equal while in diffraction the width of the central fringe is invariably different from the secondary fringes.

3) In interference, the bright fringes are of same intensity while in case of diffraction intensity of bright fringes goes on decreasing.

4) In interference, the fringes of minimum intensity are perfectly dark whereas those in case of diffraction are not perfectly dark.

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