BSA Flow Software Installation and User's Guide - CSI

n2
= arcsin , where =
n
ϕc nrel nrel
1
(A1-3)
Amplitude of The light can be split in two components: one polarized perpendicular
transmitted and (S) and one parallel (P) to the plane of incidence. Then the amplitude of
reflected light the transmitted light and of the reflected light relative to the incident light
can be estimated for both directions (Fresnel equations):
t
t
r
r
S
P
S
P
2sin ϕtcos ϕi
2n1cosϕ i
=
=
sin
n cosϕ + n cosϕ
(A1-4)
( ϕ + ϕ )
t i
( ϕ + ϕ ) ( ϕ −ϕ
)
1 i 2 t
2sin ϕtcosϕ i
2n1cos ϕi
=
=
sin cos n cosϕ + n cosϕ
(A1-5)
sin
=
sin
tan
=
tan
t i t i
( ϕi − ϕt)
( ϕ + ϕ )
i t
( ϕi − ϕt)
( ϕ + ϕ )
i t
n1cos ϕ − n2cos
ϕ
=
n cosϕ + n cosϕ
2 i 1 i
i t
1 i 2 t
n2cosϕ − n1cosϕ
=
n cosϕ + n cosϕ
i t
2 i 1 t
(A1-6)
(A1-7)
We see that for both refraction and reflection the two orientations of
polarization depend differently on the angle of incidence, ϕ i .
Brewster’s angle A special case is important. If we look at the last expression:
r P
tan
=
tan
( ϕi − ϕt)
( ϕ + ϕ )
i t
we see that if ϕi + ϕt = π 2 the denominator goes to infinity and,
consequently, the fraction becomes zero. The incident angle in this case is
called Brewster’s angle, ϕB .
By rearranging ϕ = π 2 − ϕ , and by applying Snell’s law we get:
t B
⎛ π ⎞
n1sin ϕB = n2sinϕt = n2sin⎜ −ϕB⎟
= n2cosϕB
(A1-8)
⎝ 2 ⎠
whence
ϕ B =
⎛ n ⎞
⎜ ⎟
⎝ n ⎠
arctan 2
1
(A1-9)
7-36 BSA Flow Software: Reference guide