Coupon Accepted Successfully!


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 nth secondary minima at P on the screen, path difference between the diffracted waves Δ = b sin θ = 
  • Angular position of nth secondary minima
  • Distance of nth secondary minima from central maxima
    where D = distance between slit and screen. f  D = Focal length of converging lens.

Secondary maxima

For nth secondary maxima at P on the screen.
Path difference, 95019.png; where n = 1, 2, 3 ...
  • Angular position of nth secondary maxima
  • Distance of nth 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 = 95037.png
  • Linear width of central maxima

Intensity distribution

If the intensity of the central maxima is I0, then the intensity of the first and second secondary maxima are found to be I0/22 and I0/61. Thus, diffraction fringes are of unequal width and unequal intensities.
  • The mathematical expression for intensity distribution on the screen is given by
    where α is just a convenient connection between the angle θ that locates a point on the viewing screening and light intensity I.
Fig. 17
φ = Phase difference between the top and bottom ray from the slit width b.
Also 95058.png
  • 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 > λ, 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

Test Your Skills Now!
Take a Quiz now
Reviewer Name