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Unformatted text preview: e angle, , between the two cylindrical waves remains constant. Moreover, according to Equation (1009), the interference
pattern appearing on the projection screen is produced by the phase difference
between the two cylindrical waves at a given point on the screen, and
this phase difference only depends on the relative phase angle. Indeed, the intensity of the interference pattern is
. Hence, the fact that the relative phase angle,
, between the two cylindrical waves emitted by the slits remains constant on timescales much longer
than the characteristic coherence time, , of the light source implies that the interference pattern generated in a conventional two- slit interference apparatus is unaffected by the temporal incoherence of the source. Strictly
speaking, however, the preceding conclusion is only accurate when the spatial extent of the light source is
negligible. Let us now broaden our discussion to take spatially extended light sources into account. Figure 67: Two- slit interference with two line sources.
Up until now, we have assumed that our two- slit interference apparatus is illuminated by a single plane wave,
such as might be generated by a line source located at infinity. Let us now consider a more realistic situation in
which the light source is located a finite distance from the slits, and also has a finite spatial extent.
Figure 67 shows the simplest possible case. Here, the slits are illuminated by two identical line sources,
, that are a distance
apart, and a perpendicular distance from the opaque screen containing the slits.
, the light incident on the slits from source
is effectively a plane wave whose
direction of propagation subtends an angle
the slits from source with the - axis. Likewise, the light incident on is a p...
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