Fraunhofer Diffraction by Four Slits
A metal plate in air contains four parallel slits, each of width
a
. The distance be
tween the slits is
d
with
d
= 4
a
. The metal slit plate is illuminated at normal incidence
by a plane wave of freespace wavelength
λ
. The transmittance of the slit plate is given
by
f
4
as shown in the figure. The transmittance is 100% (t = 1) within the slits and 0%
(t = 0) elsewhere.
Derive, showing all work, the amplitude of the farfield (Fraunhofer) diffraction
pattern resulting from the diffraction of the plane wave by this amplitude transmittance
function,
f
4
. Express your answer as
A
(
k
x
) where
A
(
k
x
) is a function of
a
and
k
x
only
,
where
k
x
is the
x
component of the diffracted wavevector. Derive, showing all work,
the radiant intensity of the farfield (Fraunhofer) diffraction pattern resulting from the
diffraction of the plane wave by this amplitude transmittance function,
f
4
. Express your
answer as
I
(
k
x
) where
I
(
k
x
) is a function of
I
0
,
a
, and
k
x
only
, where
I
0
is the farfield
radiant intensity at
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 Spring '08
 Gaylord
 Diffraction, Wavelength, kx

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