Page 227 - Modern Optical Engineering The Design of Optical Systems

210 Chapter Ten

index of refraction for the helium d line (0.5876 m) and the Abbe
V-number, or reciprocal relative dispersion. The V-number, or V-value,
is defined as
n d 1
V (10.15)
n n
F C
where n d , n F, and n C are the indices of refraction for the helium d line,
the hydrogen F line (0.4861 m), and the hydrogen C line (0.6563 m),
respectively*. Note that
n n F n C is a measure of the dispersion, and
its ratio with n d 1 (which effectively indicates the basic refracting
power of the material) gives the dispersion relative to the amount of
bending that a light ray undergoes.
For optical glass, these two numbers describe the glass type and are
conventionally written (n d 1):V as a six-digit code. For example, a
glass with an n d of 1.517 and a V of 64.5 would be identified as 517:645
or 517645.
For many purposes, the index and V-value are sufficient information
about a material. For secondary spectrum work, however, it is neces-
sary to know more, and the relative partial dispersion

n d n C
P (10.16)
C
n n
F C
is frequently used for this purpose. P C is a measure of the rate of
change of the slope of the index versus wavelength curve (i.e., the cur-
vature or second derivative). Note that a relative partial dispersion
can be defined for any portion of the spectrum and that most glass cat-
alogs list about a dozen partials.
The index of refraction values conventionally given in catalogs,
handbooks, etc., are those arrived at by measuring a sample piece in
air, and are thus the index relative to the index of air at the wave-
length, temperature, humidity, and pressure encountered in the mea-
surement. Since the index is used in optical calculations as a relative
number, this causes no difficulty if the index of air is assumed to be 1.0
exactly, and for all wavelengths (unless the optical system is to be used
in a vacuum, in which case the catalog index must be adjusted for the
index of air; see Sec. 1.2).

10.2 Optical Glass

Optical glass is almost the ideal material for use in the visual and near-
infrared spectral regions. It is stable, readily fabricated, homogeneous,
clear, and economically available in a fairly wide range of characteristics.

* The Fraunhofer lines of the solar spectrum are listed in Fig. 10.9.