Question

In your own words:

1. (i) Use the Huygens principle to explain how plane parallel wavefronts are diffracted at a single aperture.

2. (ii) Use the principle of superposition to explain how coherent light emerging from two narrow slits can interfere to produce a pattern on a distant screen.

Answer 1

(i) Huygens principle states that every point on a wavefront (plane or spherical or others) may be considered a source of secondary spherical wavelets which spread out in the forward direction at the speed of light. The new shape of wavefront is the tangential surface to all of these secondary wavelets after certain time interval.

In the above figure for a single slit and parallel wavefront, every point parallel to single slit will act as secondary source which will creates spherical wavefront. It will go in any direction after the slit in space. Hence, you can observe the effect of diffraction for this case.

(b)  Principle of Superposition states that the resultant displacement for two component waves can be found by adding the two displacements together: If the two monochromatic waves are in phase and with same amplitude, there will be constructive interference i.e. resultant intensity will double or bright mode, and if they are out of phase, there will be destructive interference i.e. no resultant intensity or dark mode. Superposition will occur whether waves are coherent or not. (However, if the waves are coherent, they will interfere to produce a fixed pattern.)

In the figure, let us consider the two slits are at A and B. The screen is at a distance D from the plane of the sources. You have to find the pattern at point P. The separation between the slits is a. The light will go from the sources A and B and they will meet at P. Here, superposition principle comes into play. You have to find the resultant intensity at P for two waves originating at A and B. The phase difference occurs at P for two waves due to the path difference (here the source A and B are coherent and they have zero phase difference). Now, bright fringe occurs at P if BP - AP = nλ and dark fringe occurs at P if BP - AP = (n + 1/2)λ.