Class Content  > The wave model  > Huygens' principle and the wave model

Prerequisites:

• Huygens' principle and the wave model 
• The math of Huygens' principle   
• Superposition of waves in 1D  
• Two-slit interference

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.