Rayleigh-Gans approximation
This approximation allows one to consider larger particles than in the Rayleigh regime, as long
as their relative refractive index is weak, i.e., |m-1|<<1. An additional inequality must also
hold in order to apply the Rayleigh-Gans approximation:
kL|m-1|<<1
For linearly polarized incident light, the Rayleigh-Gans approximation predicts the
scattered light intensity, in a plane parallel to the incident polarization, to be given by:
I_(P)=(pi ^(2)V^(2))/(r^(2)lambda ^(4))(m-1)^(2)(cos^(2) heta )P( heta ,lambda )
where V is the volume of the scatterer and P( heta ,lambda ), known as the "form factor", is an oscillatory
component sensitive to the scatterer geometry. For spherical scatterers with diameter L, the
form factor becomes:
P( heta ,lambda )=((9pi )/(2u^(2)))J_((3)/(2))^(2)(u)=[((3)/(u^(3)))(sinu-ucosu)]^(2)
where u=qL=2kLsin(( heta )/(2)).
Use eqns. 3 and 4 to plot the intensity of the backscattered light ( heta =180deg ) as a function of
wavelength (lambda =300-800nm) for the following biological scatterers: a large globular protein
(L=5nm), a lysosome (L=50nm) and a mitochondrion (L=0.5mu m). For simplicity, assume they
are all spherical and have the same relative refractive index, m=1.05. Overlay the spectra in a
log-log plot for comparison, normalizing the value at lambda =300nm to 1 . How do the spectra
deviate from Rayleigh scattering as the particle size increases?
Rayleigh-Gans approximation This approximation allows one to consider larger particles than in the Rayleigh regime, as long as their relative refractive index is weak, i.e., |m-l|<l. An additional inequality must also hold in order to apply the Rayleigh-Gans approximation:
kL|m-1|<<1 (2) For linearly polarized incident light, the Rayleigh-Gans approximation predicts the scattered light intensity, in a plane parallel to the incident polarization, to be given by:
-1)2(cos2 0)P(0,2)
(3)
where V is the volume of the scatterer and P(0,), known as the "form factor", is an oscillatory component sensitive to the scatterer geometry. For spherical scatterers with diameter L, the form factor becomes:
P(0,1)
sinu-ucosu
(4)
where u= qL = 2kL sin(0/2)
Use eqns. 3 and 4 to plot the intensity of the backscattered light (0=180') as a function of wavelength (=300-800nm) for the following biological scatterers: a large globular protein (L=5nm), a lysosome (L=50nm) and a mitochondrion (L=0.5um). For simplicity, assume they are all spherical and have the same relative refractive index, m=l.05. Overlay the spectra in a log-log plot for comparison, normalizing the value at 2=300nm to l. How do the spectra deviate from Rayleigh scattering as the particle size increases?
