92168.pdf

Optical properties 57

The quantity Re (1+cos^2 0) is called the Rayleigh ratio. The unity

term in (1+cos^2 0) refers to the vertically polarised component of the

scattered light, and the cos^2  0 term to the horizontally polarised

component.

Since the scattering intensity is proportional to I/A^4 , blue light (A ~

450 nm) is scattered much more than red light (A ~ 650 nin). With

incident white light, a scattering material will, therefore, tend to

appear to be blue when viewed at right angles to the incident beam

and red when viewed from end-on. This phenomenon is evident in

the blue colour of the sky, tobacco smoke, diluted milk, etc., and in

the yellowish-red of the rising and setting sun.

interparticle interference

If the scattering sources in a system are close together and regularly

spaced, as in a crystalline material, there will be regular phase

relationships (coherent scattering) and, therefore, almost total

destructive interference between the scattered light waves - i.e. the

intensity of the resulting scattered light will be almost zero. When the

scattering sources are randomly arranged, which is virtually the case

for gases, pure liquids and dilute solutions or dispersions, there are

no definite phase relationships (incoherent scattering) and destructive

interference between the scattered light waves is incomplete.

For a system of independent scatterers (point sources of scattered

light distributed completely at random), the emitted light waves have

an equal probability of reinforcing or destructively interfering with

one another. The amplitudes of the scattered waves add and subtract

in a random fashion, with the result that (by analogy with Brownian

displacement; page 25) the amplitude of the total scattered light is

proportional to the square root of the number of scattering particles.

Since the intensity of a light wave is proportional to the square of its

amplitude, the total intensity of scattered light is proportional to the

number of particles.

Relative molecular masses from light-scattering measurements

If the dimensions of a scattering particle are all less than c. A/20, the
scattered light waves emanating from the various parts of the particle
cannot be more than c. A/10 out of phase, and so their amplitudes are
practically additive. The total amplitude of the light scattered from