BSA Flow Software Installation and User's Guide - CSI

⎡ ⎛ 1 ⎞ π ⎤
1
ϕ1
= 2⎢
⎜ ⎟ − ⎥ 2
ϕ 1
⎣⎢
⎝ ⎠ 2 ⎦⎥
=
⎛ ⎞
arcsin arccos⎜
⎟ = c
nrel ⎝ nrel
⎠
(A1-17)
Second order For droplets and other particles with a relative refractive index n rel > 1,
refraction - the maximum intensity is obtained at the rainbow angle, ϕ r , i.e. the
Rainbow angle minimum angle of second order refracted light, viz. the angle where this
light folds back. The angle of a ray of second order refraction is ϕ 2 , as
expressed in equation (A1-12) above.
This angle has its minimum when:
⎧⎪
1
= −
⎩⎪ 3
ϕi arccos⎨
r
2 ( n el 1)
[ n ] [ n ]
ϕ2= 4arcsin cos( γ) / −2λ− 2π = 4arccos
cos( γ)
/
18)
which is at a minimum when:
⎧⎪
1 ⎫
⎧
γ = arccos⎨ − arcsin
⎩⎪ 3 ⎭⎪ 2 ⎩⎪
rel rel 2λ
⎫⎪
⎬
⎭⎪
2 ⎪ π ⎪ 1 2
( n 1)
⎬ + = ⎨ ( n −1)
3
⎫⎪
⎬
⎭⎪
− (A1-
rel rel (A1-19)
A special case occurs when the rainbow angle is:
⎛ ϕi
⎞
ϕr2
= 4arcsin⎜ ⎟ −2ϕi− π = π
⎝ n ⎠
sin
This occurs when :
rel
⎧⎪
⎫⎪
= ( n − ) ⎬
⎩⎪
⎭⎪ =
1 2
1 0
3
ϕi ⎨ rel
arccos
which is satisfied when:
2 ( )
(A1-21)
(A1-20)
1
nrel − 1 = 1,
i.e. when nrel
= 2 (A1-22)
3
Critical angle For a bubble (n rel < 1), there is a range of forward scattering where second
order refraction has two components in the same direction. This range is
limited by the critical incident angle for the transmission at the first
interface. Thus, for the light to be transmitted into the interior ϕ i < ϕ c .
7-40 BSA Flow Software: Reference guide