Physical Chemistry Third Edition

994 23 Optical Spectroscopy and Photochemistry

electric field oscillating in one plane and a magnetic field oscillating in a plane per-

pendicular to the first plane.Circularly polarized lightis equivalent to the sum of two

plane-polarized rays of equal amplitude and wavelength that are polarized in perpen-

dicular directions and out of phase by a fourth of a wavelength. Figure 23.21 shows

the electric field. The sum of the two electric fields follows a helix at any one instant.

If the wave shown in the figure propagates to the right of the figure, an observer facing

the source of radiation sees an electric field that rotates clockwise. Such radiation is

calledright-polarizedradiation, whereas radiation that gives a field rotating counter-

clockwise when looking into the source is calledleft-polarized radiation. Individual

photons correspond to circularly polarized light rather than to plane polarized light.

The projection of the spin angular momentum of a photon can equal eitherh ̄(parallel

to its direction of propagation) or−h ̄(antiparallel to it), and these two possibilities

correspond to the two directions of circular polarization.

It is also possible to depict plane polarized light as being made up of equal numbers

of left circularly polarized photons and right circularly polarized photons. Figure 23.22a

shows the rotation of the electric fields of a right-polarized ray and a left-polarized ray

at a fixed location. As the two electric field contributions rotate in opposite directions

their sum will remain in a plane if they are in phase and have the same frequency and

the same amplitude.

As light passes through a transparent medium, its speed is less than the speed of

light in a vacuum. This can be thought of as absorption of the light by the molecules or

atoms of the medium followed by re-radiation in the same direction as before, slowing

the propagation of the light. Therefractive index,n, of a medium is defined as the ratio

of the speed of light in a vacuum to the speed of light in the medium:

n

c(vacuum)

c(medium)

(definition of refractive index) (23.8-2)

The refractive index depends on the wavelength of light as well as on the identity of

the medium.

Molecules that have a plane of symmetry interact with photons of both circular

polarizations in the same way. A molecule without a plane of symmetry appears different

to the two kinds of photons, and the speed of light of the two kinds of photons can

be different. The rotation of one circularly polarized electric field contribution lags

behind the other, and the plane of polarization is rotated as shown in Figure 23.22b.

Electric

field vector

z

y

x

Direction of propagation

Figure 23.21 Circularly Polarized Light from Plane-Polarized Light.The circularly

polarized light corresponds to the electric field vector moving in a helical pattern.