I understand that diffraction is the bending of light around sharp edges. Using Huygens' theory, one explains this by imagining a plane wave hitting a slit. Normally, each point on the plane wave would act as a spherical wavefront, and the common envelope of all these wavefronts would also be a plane wave. When part of this wave is blocked by an obstacle,the 'top-most or bottom-most' part of the new wave would propagate spherically as there is no longer anything above or below, to flatten the wavefront. Hence, our wavefront now looks more like this:
I know this can also be explained using the uncertainty principle, but my goal is to understand Huygens' theory properly.
Anyway, as we can see, the wavefront spreads into the geometric shadow. Now, all this is well and good, but I don't seem to understand where do the 'fringes' come from. Huygen's theory seems to explain why light bends around obstacles, but not why we should get a fringe pattern in case of a single slit.
Many books suggest, this is because the secondary sources on this new 'semi-circularish' wave-front, produce spherical waves that interfere with one another, to create points of constructive and destructive interference. This self interaction doesn't seem to make sense to me.
In case of the simple double slit experiment, the idea of two separate wavefronts interfering with each other to create bright and dark bands seem to make sense.
But now, imagine a single source from which the wavefront spreads in all directions i.e. a source with a spherical wavefront. Now suppose, there is a screen in front of the source. There would be an uniform intensity distribution on the screen. However, if I now put a single slit between the source and the screen, the intensity pattern would show fringes. The case with the slit is explained by saying that after the wave comes out of the slit, each point acts as a secondary source, and the waveforms from these sources interfere constructively and destructively. However, if there was no slit, even then each point on the spherical wavefront would act as secondary source. However, we don't consider the interference of the waves from these secondary sources in the absence of a slit. Else, we would get a bright and dark band pattern by simply shining light on an object.
In any scenario, each point on a wavefront, acts as a secondary source. However, after passing through an obstacle, these secondary sources interfere with each other to create bright and dark patterns. But using this logic, if we just consider the simple spreading out of light from a point source, then each point on this spherical wavefront should also act as secondary sources which should interfere with each other. However, this would cause a diffraction patter on any screen irrespective of the presence of an obstacle.
Can anyone help me understand this.
( I know how the fringes appear using integration over a wave and then finding conditions of maxima and minima. I just want to understand this, by using huygens principle ). If light interferes with itself, then shouldn't we see dark and bright bands everywhere ? Why do we need a slit?
Best Answer
Huygens' principle does not explain interference. It applies to incoherent waves. You need wave theory to describe interference which results from wave coherence.
"Else, we would get a bright and dark band pattern by simply shining light on an object." These bands exist but they move with the speed of light or alternate with the frequency of the light. They do not form a stationary interference pattern.
We need a perturbation such as a slit to get a stationary pattern.