# Diffraction at Single Slit (Fraunhoffer Diffraction)

Suppose a plane wave front is incident on a slit

*AB*(of width*b*). Each and every part of the expose part of the plane wave front (i.e., every part of the slit) acts as a source of secondary wavelets spreading in all directions. The diffraction is obtained on a screen placed at a large distance. (In practice, this condition is achieved by placing the screen at the focal plane of a converging lens placed just after the slit).**Fig. 15**

- The diffraction pattern consists of a central bright fringe (central maxima) surrounded by dark and bright lines (called secondary minima and maxima).
- At point
*O*on the screen, the central maxima is obtained. The wavelets originating from points*A*and*B*meets in the same phase at this point, hence at*O*, intensity is maximum.

# Secondary minima

For obtaining

*n*th secondary minima at*P*on the screen, path difference between the diffracted waves Î” =*b*sin*Î¸*=*nÎ»*- Angular position of
*n*th secondary minima - Distance of
*n*th secondary minima from central maxima*D*= distance between slit and screen.*f*â‰ˆ*D*= Focal length of converging lens.

# Secondary maxima

For

*n*th secondary maxima at*P*on the screen.Path difference, ; where

*n*= 1, 2, 3 ...- Angular position of
*n*th secondary maxima - Distance of
*n*th secondary maxima, from central maxima

# Central maxima

The central maxima lies between the first minima on both sides.

**Fig. 16**

- Angular width
*d*central maxima = - Linear width of central maxima

# Intensity distribution

If the intensity of the central maxima is

*I*_{0}, then the intensity of the first and second secondary maxima are found to be*I*_{0}/22 and*I*_{0}/61. Thus, diffraction fringes are of unequal width and unequal intensities.- The mathematical expression for intensity distribution on the screen is given by
*Î±*is just a convenient connection between the angle*Î¸*that locates a point on the viewing screening and light intensity*I*.

**Fig. 17**

*Ï†*= Phase difference between the top and bottom ray from the slit width

*b*.

- As the slit width increases (relative to wavelength), the width of the control diffraction maxima decreases; that is, the light undergoes less flaring by the slit. The secondary maxima also decreases in width (and becomes weaker).
- If
*b*>*Î»*, the secondary maxima due to the slit disappear; we then no longer have single slit diffraction. - When the slit width is reduced by a factor of 2, the amplitude of the wave at the centre of the screen is reduced by a factor of 2, so the intensity at the centre is reduced by a factor of 4.

**Fig. 18**