28
Physics Formulary by ir. J.C.A. Wevers
The dispersion of a prism is defined by:
D
=
d
δ
d
λ
=
d
δ
dn
dn
d
λ
where the first factor depends on the shape and the second on the composition of the prism. For the first factor
follows:
d
δ
dn
=
2 sin(
1
2
α
)
cos(
1
2
(
δ
min
+
α
))
For visible light usually holds
dn/d
λ
<
0
: shorter wavelengths are stronger bent than longer. The refractive
index in this area can usually be approximated by Cauchy’s formula.
6.8
Diffraction
Fraunhofer diffraction occurs far away from the source(s). The Fraunhofer diffraction of light passing through
multiple slits is described by:
I
(
θ
)
I
0
=
sin(
u
)
u
2
·
sin(
Nv
)
sin(
v
)
2
where
u
=
π
b
sin(
θ
)
/
λ
,
v
=
π
d
sin(
θ
)
/
λ
.
N
is the number of slits,
b
the width of a slit and
d
the distance
between the slits. The maxima in intensity are given by
d
sin(
θ
) =
k
λ
.
The diffraction through a spherical aperture with radius
a
is described by:
I
(
θ
)
I
0
=
J
1
(
ka
sin(
θ
))
ka
sin(
θ
)
2
The diffraction pattern of a rectangular aperture at distance
R
with length
a
in the
x
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 Spring '10
 Ye
 Physics, Sin, Diffraction pattern, Fraunhofer diffraction, n1, Optical axis

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