BSA Flow Software Installation and User's Guide - CSI

Figure 7-36: The critical angle condition illustrated for a droplet of water.
In the border case when ϕ i = ϕ c , the light will be refracted out again at the
same point and in the direction:
( n )
ϕ = 2arccos
= ϕc
(A1-23)
c2 rel 1
Again, for a droplet (n rel > 1), the critical angle expresses that light from the
interior will be transmitted to the exterior only when the incident angle ϕ i <
π/2.
Under critical conditions the scattering angle of second order refracted light
is:
⎛ 1 ⎞
ϕ2 = 4 arcsin⎜ ⎟ − 2π
= ϕ c 2
(A1-24)
⎝ nrel ⎠
ϕ
c2
⎡ ⎛ 1 ⎞ π ⎤
1
= 4⎢
⎜ ⎟ − ⎥ 4
⎣⎢
⎝ nrel ⎠ 2 ⎦⎥
nrel
=
⎛ ⎞
arcsin arccos ⎜ ⎟ (A1-25)
⎝ ⎠
When the critical angle ϕ c2 < π, the range of the scattering angles between
the rainbow angle and the critical angle will have two components of second
order refracted light.
For critical angles ϕ c2 > π, the range ϕ r2 –2π to ϕ c2 has two components,
while the range 2π to ϕ c2 –π has three components.
The special case ϕ c2 = π occurs when:
( ) n
ϕc2= 4arccos 1/
rel
= π
(A1-26)
( )
nrel = 1/cos π / 4 = 1.
414 (A1-27)
Third order Similar to second order refraction, third order refraction has a rainbow
BSA Flow Software:Reference guide 7-41