Chapter 4 – Making Light Work Harder in Biology  141

wavelength though it has a complex formulation, but the two extremes of this at very short

(Rayleigh) and very high (geometrical) wavelength generate the following approximations,

first for Rayleigh, σR,

(4.21)

σ

π

λ

R

r

r

=

−

+



^



^

128

3

1

2

6

4

2

2

2

r

n

n

and for geometrical scattering, σG,

(4.22)

σ

π

G ^{= r 2}

where nr is the ratio of refractive indices for the scattering particle and its surrounding media,

nb/​nw, where nb is the refractive index of the biological scattering object and nw is the refractive

index of water. In other words, the cross-​section for Rayleigh scatterers scale with ~V ² where

V is their volume, whereas for geometrical scatterers this dependence with volume is much

less sensitive at ~V^2/​3.

KEY POINT 4.4

“Geometrical” (i.e., ballistic type) scattering applies for effective diameter r > 10λ, Mie/​

Tyndall scattering for ~0.1λ < r < 10λ and Rayleigh scattering for ~r > 0.1λ. For an elec­

tric dipole, the polarizability p is proportional to an incident sinusoidal E-​field plane

FIGURE 4.4  Nonlinear excitation and inelastic scattering: (a) Jablonski diagram for two-​

photon excitation. (b) Schematic of static light scattering apparatus. (c) Jablonski diagram

for several inelastic light scattering modes compared against elastic Rayleigh scattering.

(d) Schematic of Raman imaging spectrophotometer (typically based on a scanning confocal

microscope core design).