phy1020.DVI

Chapter 54

Dispersion

Recall that the index of refractionnof a transparent material is the ratio of the speed of light in vacuum to
the speed of light in the material:nDc=v. In general, the index of refraction will vary somewhat with
wavelength; this phenomenon is calleddispersion. Dispersion can be an unwanted effect in lenses, since it
causes chromatic aberration. But it can also be useful in prisms, in that it allows “white” light (light of all
wavelengths) to be separated into its component colors. The same phenomenon occurs in Nature, where the
dispersion properties of water allows sunlight to be separated into its component colors by water droplets,
resulting in arainbow.
For example, the

54.1 Cauchy Dispersion Formula

One simple model for dispersion in materials is theCauchy dispersion formula:

n./Da 0 C

a 1

2

C

a 2

4

C

a 3

6

C (54.1)

One often uses just the first two terms of the Cauchy dispersion formula:

n./Da 0 C

a 1

2

; (54.2)

where is the wavelength, and the constantsandepend on the material.
For water ( 20 ıC),a 0 D1:31494,a 1 D4537:99465nm^2.
Three terms:

n./Da 0 C

a 1

2

C

a 2

4

; (54.3)

where is the wavelength, and the constantsandepend on the material.
For water ( 20 ıC),a 0 D1:32692,a 1 D1610:845nm^2 ,a 2 D 95402300 nm^4.

54.2 Sellmeier Dispersion Formula

A more complex dispersion model is called theSellmeier dispersion formula:

n./D



1 C

B 12

2 C 1

C

B 22

2 C 2

C

B 32

2 C 3

1=2

; (54.4)