Physical Chemistry Third Edition

23.8 Other Types of Spectroscopy 995

Etot 5 Er 1 El

Etot

Etot

Etot

Etot

Etot

Etot

Etot

Etot

Etot

El Er

Er

Er Er Er

Er

El El El

El El

El Er El Er Er El Er El

Time: t 1 t 2 t 3

(a)

t 4 t 5

Time: t 1 t 2 t 3

(b)

t 4 t 5

Angle of

rotation

Figure 23.22 Plane-Polarized Light (Etot)from Right-Polarized Light (Er)and Left-

Polarized Light (El).(a) Plane-polarized light in a vertical plane. This diagram shows how

the two vectors from the right- and left-polarized light add to produce a sum vector that

oscillates in one plane. (b) Plane-polarized light (Etot) from right-polarized light (Er) and

left-polarized light (El) which is delayed relative to that in Figure 23.22a. This diagram

shows how the two vectors from the right- and left-polarized light add to produce a sum

vector that oscillates in one plane. Since one of the beams is delayed, the sum vector

oscillates in a different plane from that of (a).

This phenomenon is calledcircular birefringence, and the substance is said to be

optically active. The angleαthrough which the plane is rotated is proportional to the

length of the sample and to the difference between the refractive indexes of right- and

left-polarized light. It is given by

α

π(nR−nL)L

λ

(23.8-3)

wherenRis the refractive index for right-polarized light andnLis the refractive index

for left-polarized light of the wavelengthλand whereLis the length of the sample.

The rotating power of an optically active substance is commonly expressed as the

specific rotation[α], defined by

[α]α/ρL (definition) (23.8-4)

whereαis the angle of rotation,ρis the density of the substance, andLis the length of

the sample. If one has a solute in solution, the density is replaced by the concentration

of the substance. The specific rotation depends on the identity of the substance, the

identify of the solvent (if any), the temperature, and the wavelength of light.