## ASTM C1648 – **Standard Guide for Choosing a Method for Determining the Index of Refraction and Dispersion of Glass**

**Description**:

Significance and Use

4.1 Measurement—The refractive index at any wavelength of a piece of homogeneous glass is a function, primarily, of its composition, and secondarily, of its state of annealing. The index of a glass can be altered over a range of up to 1×10^{-4} (that is, 1 in the fourth decimal place) by the changing of an annealing schedule. This is a critical consideration for optical glasses, that is, glasses intended for use in high performance optical instruments where the required value of an index can be as exact as 1×10^{-6}. Compensation for minor variations of composition are made by controlled rates of annealing for such optical glasses; therefore, the ability to measure index to six decimal places can be a necessity; however, for most commercial and experimental glasses, standard annealing schedules appropriate to each are used to limit internal stress and less rigorous methods of test for refractive index are usually adequate. The refractive indices of glass ophthalmic lens pressings are held to 5×10^{-4} because the tools used for generating the figures of ophthalmic lenses are made to produce curvatures that are related to specific indices of refraction of the lens materials.

4.2 Dispersion—Dispersion-values aid optical designers in their selection of glasses (Note 1). Each relative partial dispersion-number is calculated for a particular set of three wavelengths, and several such numbers, representing different parts of the spectrum might be used when designing more complex optical systems. For most glasses, dispersion increases with increasing refractive index. For the purposes of this standard, it is sufficient to describe only two reciprocal relative partial dispersions that are commonly used for characterizing glasses. The longest established practice has been to cite the Abbe-number (or Abbe ν-value), calculated by:

where *v _{D}* is defined in 3.2 and

*n*,

_{D}*n*, and

_{F}*n*are the indices of refraction at the emission lines defined in 3.2.

_{C}4.2.1 Some modern usage specifies the use of the mercury e-line, and the cadmium *C*′ and *F*′ lines. These three lines are obtained with a single spectral lamp.

where *v _{e}* is defined in 3.2 and

*n*,

_{e}*n*, and

_{F′}*n*are the indices of refraction at the emission lines defined in 3.2.

_{C′}4.2.2 A consequence of the defining equations (Eq 1 and 2) is that smaller ν-values correspond to larger dispersions. For ν-values accurate to 1 % to 4 %, index measurements must be accurate to 1×10^{-4}; therefore, citing ν-values from less accurate test methods might not be useful.

NOTE 1: For lens-design, some computer ray-tracing programs use data directly from the tabulation of refractive indices over the full wavelength range of measurement.

NOTE 2: Because smaller ν-values represent larger physical dispersions, the term constringence is used in some texts instead of dispersion.

Scope

1.1 This guide identifies and describes seven test methods for measuring the index of refraction of glass, with comments relevant to their uses such that an appropriate choice of method can be made. Four additional methods are mentioned by name, and brief descriptive information is given in Annex A1. The choice of a test method will depend upon the accuracy required, the nature of the test specimen that can be provided, the instrumentation available, and (perhaps) the time required for, or the cost of, the analysis. Refractive index is a function of the wavelength of light; therefore, its measurement is made with narrow-bandwidth light. Dispersion is the physical phenomenon of the variation of refractive index with wavelength. The nature of the test-specimen refers to its size, form, and quality of finish, as described in each of the methods herein. The test methods described are mostly for the visible range of wavelengths (approximately 400 μm to 780 μm); however, some methods can be extended to the ultraviolet and near infrared, using radiation detectors other than the human eye.

1.1.1 List of test methods included in this guide:

1.1.1.1 Becke line (method of central illumination),

1.1.1.2 Apparent depth of microscope focus (the method of the Duc de Chaulnes),

1.1.1.3 Critical Angle Refractometers (Abbe type and Pulfrich type),

1.1.1.4 Metricon2 system,

1.1.1.5 Vee-block refractometers,

1.1.1.6 Prism spectrometer, and

1.1.1.7 Specular reflectance.

1.1.2 Test methods presented by name only (see Annex A1):

1.1.2.1 Immersion refractometers,

1.1.2.2 Interferometry,

1.1.2.3 Ellipsometry, and

1.1.2.4 Method of oblique illumination.