Chemistry Reference
In-Depth Information
The vibration that propagates along Ox is retarded compared to the one
that propagates along Oy of a quantity:
2
π
φ
=
2
π
e (n
γ
n
α
)/cT
=
2
π
e (n
γ
n
α
)/
λ
where
cT is the wave length.
The two vibrations are recomposed at the exit of the plate into an ellip-
tically polarized vibration: a plane polarized wave is transformed by the pas-
sage through a parallel plate of an anisotropic medium into an elliptically
polarized wave .
Means a change of variables, the equation of this wave at the exit of
the plate is:
λ
=
Ox
=
a cos
α
sin2
π
(t/T
φ
)
Oy
=
a sin
α
sin2
π
t/T
with
λ
This vibration then passes through the analyser (upper polarizer) whose
polarization plane makes an angle
φ
=
e (n
γ
n
α
)/
with the one of the (lower) polarizer.
The vibration in the plane of the analyser will be:
β
OA
=
Ox cos
β
+
Oy sin
β
=
a cos
α
cos
β
sin2
π
(t/T
φ
)
+
a sin
α
sin
β
sin2
π
t/T
Practically the Nicols are at right angle:
β
=
α
+
π
/2
OA
=
a cos
α
cos (
α
+
π
/2) sin2
π
(t/T
φ
)
+
a sin
α
sin (
α
+
π
/2) sin2
π
t/T
OA
=
a cos
α
sin
α
sin2
π
(t/T
φ
)
+
a sin
α
cos
α
sin2
π
t/T
OA
=
a sin
α
cos
α
[sin2
π
t/T
sin2
π
(t/T
φ
)]
AS sin p
sin q
=
2cos (p
+
q)/2 sin (p
q)/2
OA
=
a 2 sin
α
cos
α
[cos 2
π
(t/T
φ
/2) sin
πφ
]
OA
=
a sin 2
α
sin
πφ
[cos 2
π
(t/T
φ
/2)]
The amplitude of this vibration is thus:
a sin 2
α
sin
πφ
=
a sin2
α
sin(
π
e (n
γ
n
α
)/
λ
)
As the intensity is proportional to the square of the amplitude, the inten-
sity at the exit will be:
a 2 sin 2 2
α
sin 2 (
π
e ( n
γ
n
α
)/
λ
)
δ
=
(n
γ
n
α
) is the birefringence of this section
a 2 sin 2 2
α
sin 2 (
π
e
δ
/
λ
)
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