what is the formula for fringe width in a diffraction pattern? how does it vary for minimum, maximum? and also how is it different from the formula for fringe width in interference pattern?
Diffraction at a single slit (Fraunhofer diffraction)
The phenomenon of bending of light round the sharp corners of an obstacle and spreading into the regions of the geometrical shadow is called diffraction.
Expression For Fringe Width
Consider a parallel beam of light from a lens falling on a slit AB. As diffraction occurs, the pattern is focused on the screen XY with the help of lens L2. We will obtain a diffraction pattern that is a central maximum at the centre O flanked by a number of dark and bright fringes called secondary maxima and minima.
Central Maximum ? Each point on the plane wave front AB sends out secondary wavelets in all directions. The waves from points equidistant from the centre C lying on the upper and lower half reach point O with zero path difference and hence, reinforce each other producing maximum intensity at point O.
Positions and Widths of Secondary Maxima and Minima
Consider a point P on the screen at which wavelets travelling in a direction making angle ? with CO are brought to focus by the lens. The wavelets from points A and B will have a path difference equal to BN.
From the right-angled ?ANB, we have
BN = AB sin ?
BN = a sin ? �(i)
Suppose BN = ? and ? = ? 1
Then, the above equation gives
? = a sin ? 1
Such a point on the screen will be the position of first secondary minimum.
If BN = 2 ? and ? = ? 2, then
2 ? = a sin ? 2
Such a point on the screen will be the position of second secondary minimum.
In interference pattern , fringe width is given by:
The fringe width is given by
? = ?D/d
?=fringe width, D= distance between slits and screen , d=distace between slits and also,?= wavelength