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Interference from many
light sources.
If we have
a plate with regularly spaced openings arranged in linear fashion we can
observe more complex interference patterns. In such an arrangement
we get constructive interference in the forward direction from the plate.
As well as in the same directions that would give constructive interference
from 2 nearest openings, if the light is in phase with that from its nearest
neighbors, then light from all sources is in phase. For example,
at some angle the first crest emitted by a given opening is in phase with
second crest emitted by the first neighbor, and with 3rd crest emitted
by 2nd neighbor and so on. Thus, on a distant screen, bright
fringes occur at the same spacing which are quiet bright, since all of
the beams interfere constructively.
Destructive interference is somewhat different. A light
source can cancel with its nearest neighbor as well as a neighbor 5 doors
down. Thus we can get many places where light interferes completely.
We have 200 regularly spaced openings, each acting as a light source.
The smallest angle of cancellation occurs when source 1 is out of phase
with source 101, source 2 with source 102, etc. So at 1/200 of the
distance between the central fringe and the first bright fringe the intensity
already dropped to zero. Because there are so many possible bright
fringes, they are very narrow. Between bright fringes, there are
many dark fringes, because there are many different ways for light to destructively
interfere. Between dark fringes there is little brightness, because
the sources are never all in phase.
The spacing
of fringes on a screen distance D away from plate can be found by multiplying
wavelength of light by D and dividing that product by spacing between light
sources. Spacing = lD/d
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