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?

Asked by Sheetal M G | 29th Mar, 2013, 08:16: PM

Expert Answer:

Diffraction
  • 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

Answered by  | 30th Mar, 2013, 10:54: AM

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