BSA Flow Software Installation and User's Guide - CSI

⎛ ϕ ⎞
ϕ2
= 4arcsin⎜ ⎟ −2ϕ −π
⎝ ⎠
sin i
i
n
rel
(A1-12)
Refracted light - For a bubble (n rel < 1), the critical angle determines whether the incident
importance of light at the first interface will be transmitted into the interior. Thus,
transmission
critical angle will take place only when the incident angle is less than the critical angle:
( n )
ϕ < ϕ = arcsin (A1-13)
i c rel
In the border case, when ϕ i = ϕ c (Figure 7-35), the light will be refracted out
again at the same point and in the direction:
⎛ π
⎞
ϕ1 = ( π−ϕc) − ϕc=
2 ⎜ −arcsin
( nrel
) ⎟ = ϕc1
(A1-14)
⎝ 2
⎠
Figure 7-35: Near critical angle condition for a bubble of air in water.
Approaching closer to the critical angle condition (arrows) brings closer together
the points where reflected, refracted and second order refracted light is emitted.
Hence,
( n )
ϕc1= 2arccos
r
el (A1-15)
For a droplet (n rel > 1), the critical angle ϕ c = arcsin(1/n rel ) determines
whether light from the interior when hitting the second interface will be
transmitted out to the exterior. Thus, transmission will take place only when
the incident angle is less than π/2:
π
ϕi < arcsin( nrelsin
ϕc)
=
2 (A1-16)
The direction of the refracted light then becomes:
BSA Flow Software:Reference guide 7-39