Class Content > The wave model > Huygens' principle and the wave model
Prerequisites:
In our study of interference between waves generated from two sources we assumed that each of our slits were points. We did not consider the possibility that the distance between the slit and the observation point might vary significantly. What does "significantly" mean here? When can we really ignore the width of the slits? Since what we were doing in the two source analysis was to compare the distances from the source to the observation point -- on scales of the order of a wavelength -- we might reasonably assume that the following works:
A source may be treated as a point for purposes of considering interference as long as the path difference from different parts of the source don't change more than a small fraction of a wavelength.
Note that this does NOT say "as long as the slit is small compared to the size of a wavelength." (We've put a strikethrough this to emphasize that that's not what matters -- and to discourage anyone from cutting and pasting the statement and forgetting to include the "NOT".) It might be just fine to ignore the size of a source that is many wavelengths large if the observation point is far enough away and in the right place.
This tells us why for a 20-cm-wide speaker putting out sound at middle C (262 Hz → λ = v0/f = [(343 m/s)/(262 1/s)] = 1.3 m) at 2 meters away it is OK to ignore the width of the speaker, but for a laser putting light through a 1/4 mm slit at λ = 600 nm, it is NOT OK to ignore the width of the slit at 2 meters away.
For this webpage, we consider the effect of the width of the source on an interference pattern. We begin by showing that a single slit can all by itself produce an interference patters -- as a result of wavelets coming from different parts of the slit interfering with each other.
What is "diffraction"?
The term diffraction was invented to describe the observation (made in the 17th century) that light didn't appear to travel exactly in straight lines. Near the edge of a shadow was a (typically small) blurring of the edge. Introductory physics texts tend to use the term "diffraction" to refer to the interference pattern coming from a single source and "interference" to refer to the pattern coming from a multiple source. But what is "single" and what is "multiple" is in the eye of the beholder and is not absolute. Is the interference of x-rays scattered from two different molecules in a crystal "interference" (because it is from two molecules) or "diffraction" (because it is from one crystal)? In his famous introductory physics text, physicist Richard Feynman says (quoted in Wikipedia)
"no-one has ever been able to define the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no specific, important physical difference between them."
and the Wikipedia article on diffraction refers to what we have called two-slit interference as "interference pattern from two-slit diffraction". In these pages we will mostly use the term "interference" when we mean the combination of two or more waves from sharply identified sources, and "diffraction" when we mean the interference pattern produced by an extended source. But don't get hung up trying to define these terms too precisely.
Single-slit diffraction: Internal interference from a single slit
To consider the effect of the non-0 size of a source of waves, we'll use the example used in our webpage, Two-slit interference: a laser beam incident on a narrow slit producing a pattern on a screen that is much farther away than the size of the slit -- or than the wavelength of the wave.
In Huygens' model of wave propagation, each point on a wavefront acts as a source of outgoing spherical waves or wavelets; and the resulting wavefront is the integral of all these wavelets. To see what this implies for a slit of non-negligible width, take a look at the figure at the right.
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