Sun February 27, 2011 By: Piyush Bansal

How is Huygens Principle used to obtain the diffraction pattern due to a single slit? And Also state the reason for the reduction in intensity of secondary maxima compared to central maximum.

Expert Reply
Mon February 28, 2011
Dear student,

periodic mechanical wave is a periodic disturbance that moves through a medium.  The medium itself goes nowhere.  The individual atoms and molecules in the medium oscillate about their equilibrium position, but their average position does not change.  As they interact with their neighbors, they transfer some of their energy to them.  The neighboring atoms in turn transfer this energy to their neighbors down the line.  In this way the energy is transported throughout the medium, without the transport of any matter.

Each point on a wavefront can therefore be considered a point source for the production of new waves.  In three dimensions, these new waves are spherical waves called wavelets, that propagate outward with the speed characteristic of waves in the medium.  The wavelets emitted by all points on the wavefront interfere with each other to produce the traveling wave.  This is called Huygens' principle.  It also holds for electromagnetic waves. 

When light passes through a small opening, comparable in size to the wavelength l of the light, in an otherwise opaque obstacle, the wavefront on the other side of the opening resembles the wavefront shown below.


The light spreads around the edges of the obstacle.  This is the phenomenon of diffraction.  Diffraction is a wave phenomenon and is also observed with water waves in a ripple tank.
When light passes through a single slit whose width w is on the order of the wavelength of the light, then we observe a single slit diffraction pattern.  Huygen's principle tells us that each part of the slit can be thought of as an emitter of waves.  All these waves interfere to produce the diffraction pattern.
For light leaving the slit in a particular direction, we may have destructive interference between the ray at the top edge (ray 1)and the middle ray (ray 5).  If these two rays interfere destructively, so do rays 2 and 6, 3 and 7, and 4 and 8.  In effect, light from one half of the opening interferes destructively and cancels out light from the other half.  Ray 1 and ray 5 are half a wavelength out of phase if ray 5 must travel 1/2 wavelength further than ray 1.
Hope this helps.
Thanking you
Ask the Expert