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Unformatted text preview: the two interference patterns reinforce one another, and the net interference pattern is the same as that generated by a light source of negligible
Suppose that our light source consists of a regularly spaced array of very many identical incoherent line sources,
filling the region between the sources
in Figure 67. In other words, suppose that our light source is a
uniform incoherent source of angular extent
. As is readily demonstrated, the associated interference pattern
is obtained by averaging expression (1016) over all
expression with values in the range 0 to : that is, by operating on this . In this manner, we obtain (1017) where . We can conveniently parameterize the v isibilit y of the interference pattern, appearing on the projection screen, in terms of the quantity (1018) where the maximum and minimum values of the intensity are taken with respect to variation in
). Thus, corresponds to a sharply defined pattern, and (rather than to a pattern that is completely washed out. It follows from Equation (1017) that (1019) The predicted visibility, , of a two- slit interference pattern generated by an extended incoherent light source is plotted as a function of the angular extent,
visible (i.e., ) when , of the source in Figure 68. It can be seen that the pattern is highly
, but becomes washed out (i.e., ) when . Figure 68: Visibility of a two- slit far- field interference
pattern generated by an extended incoherent light source.
We conclude that a spatially extended incoherent light source only generates a visible interference pattern in a
conventional two- slit interference apparatus when the angular extent of the source is sufficiently small that (1020) Equivalently, if the source is of linear extent
, and located a distance from the slits, then the source only
generates a visible interference pattern when it is sufficiently far away from the slits that (1021) This follows because . The whole of the preceding discussion is premised on the assumption that an extended light source is both...
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