| Finding the diffraction
minima is a geometric problem similar to interference,
except we are solving for the locations of the dark spots
only. (It's mathematically much more difficult to solve
for diffraction bright spots.)
Be sure to understand the geometry of interference
and diffraction using the drawings in your notes or
from the book. The bottom line is that if the slit has
a width called "a", then the location of the
first dark spot is found by:
a sin θ = λ and
tan θ = y / D
which gives:
y = λD / d
As in interference, D is the distance to the screen
and y is the distance from the CENTER of the screen
to the first dark spot. Likewise, the distance to the
m th dark spot is turns out to be:
y = m λD / d (for m = 1, 2, 3, etc., not for m = 0)
Note the similarity in the relations for interference
and diffraction:
d sin θ = mλ (maxima
for: m = 0, 1, 2, etc.)
a sin θ = mλ (minima
for: m = 1, 2, 3, etc, not for m = 0)
Both give the same general form for y, too:
y = mλD / d
(maxima for: m = 0, 1, 2, etc.)
y = mλD / a
(minima for: m = 1, 2, 3,etc., not for m = 0)
Remember:
--- if you are talking about the slit WIDTH, that's
"a", and you are solving for a dark spot
or the diffraction minima.
--- if you are talking about the slit SEPARATION,
that's "d", and you are solving for a bright
spot or the interference maxima.
Back to the photo of interference and diffraction together:
How could you make the pattern be ONLY interference?
Remember that θ
is the angular separation from the center to
the minima. Solve for θ
in the diffraction relation and see what happens if
"a" gets close to and then smaller than the
wavelength of light.
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