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Unformatted text preview: lane wave whose direction of propagation subtends an angle with the - axis. Moreover, the net interference pattern (i.e., wavefunction) appearing on the projection screen is the linear
superposition of the patterns generated by each source taken individually (because light propagation is ultimately
governed by a linear wave equation with superposable solutions- - see Section 8.2.). Let us determine whether
these patterns reinforce, or interfere with, one another.
The light emitted by source has a phase angle, characteristic coherence time of the source,
longer than between , but is subject to abrupt random changes on timescale much . Likewise, the light emitted by source much less than , that is constant on timescales much less than the has a phase angle, , and varies significantly on timescales much greater than and , that is constant on timescales
. In general, there is no correlation . In other words, our composite light source, consisting of the two line sources , is both temporally and spatially incoherent on timescales much longer than . and Again working in the limit , with , Equation (1010) yields the following expression for the wavefunction at the projection screen: (1014) Hence, the intensity of the interference pattern is (1015) However, , and
, because the phase angles and are uncorrelated. Hence, the previous expression reduces to (1016) where use has been made of the trigonometric identities , and
. (See Appendix B.) If then and . In this case, the bright fringes of the interference pattern generated by source
exactly overlay the dark fringes of the pattern generated by source
interference pattern is completely washed out. On the other hand, if
and , and vice versa, and the net
then . In this case,...
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