February 1968 L E T T E R S T O T H E E D I T O R 277

Proposed Reference Index for Typical American Glasses

P. RAJAGOPALΛ RAO, R. N. CHATTERJEE, AND D. V. SINGH Dept. of Physics, Delhi College of Engineering, Delhi 6, India

(Received 6 March 1967)

INDEX HEADINGS: Glass; Refractive index; Dispersion; Wavelengths; Refractometry.

IN the present paper we propose the mercury green line, 5461 Å, as a mean-reference-index line for typical Bausch & Lomb,

Eastman Kodak, and Corning glasses in place of the conventional sodium-D mean, 5893 Å, for dispersion studies between the F

TABLE I. nms values calculated from Eq. (2) and Eq. (4) compared with index values for the e(5461 Å) line.

FIG. 1. (1-52) vs sin2(A/2) for typical crown glasses. Bausch & Lomb (523 586, 513 605), Corning (8361, 8348).

and C lines. The mean-reference-index nms values calculated on the basis of dispersion data for these glasses, and interpolated on n vs λ curves, confirm the proposed reference index. We further confirm that the mean-reference-index values for these glasses are independent of the prism angle for angles between 20 and 60.

Optical glass is usually specified by its mean refractive index for the sodium-D mean, 5893 Å, for American glasses, and Jena glasses and by its mean refractive index for the helium d line, 5876 Å, for Chance Pilkington glasses, for dispersion between the F and C lines. However, the Jena glasses catalogue gives partial dispersion data on the basis of the mercury e line, 5461 Å, as the mean reference line for dispersion between Cadmium F', 4800 Å, and C 6438 Å lines to meet the request of some manufacturers. The choices of these lines seem to be arbitrary. Rao1 proposed a mean reference index nms for a prism material for F and C dis­persion which eliminated this arbitrary choice and involved the angle of the prism. Shah and Rao2 calculated average nms values by graphical methods using dispersion data of a number of typical Schott glasses. These nms values are seen to correspond to a wave­length of 5500±25 Å in the green region of the spectrum. Since in this region the mercury green e line, 5461 Å, is strong, we pro­pose that it may be taken as a more accurate mean-reference-index line for the F and C dispersion. In this paper optical data for typical Bausch & Lomb, Eastman Kodak, and Corning glasses3

are used to find the mean-reference-index values by the methods2

previously proposed, thus confirming the general applicability of the mercury e 5461-Å line as the mean-reference-index line for specifying optical glass by its reference index and its v number.

The mean reference index1 was defined as

278 L E T T E R S TO T H E E D I T O R Vol. 58

FIG. 2. (1 -δ2) va sin2(A./2) for typical flint glasses. Bausch & Lomb (573 425, 580 410), Corning (8327, 8371), Eastman Kodak (110,330).

F IG. 3. n vs λ for typical crown glasses. Bausch & Lomb (513 605, 523 586), Corning (8348, 8361).

FIG. 4. n vs λ for typical flint glasses. Bausch & Lomb (573 425, 580 410), Corning (8327, 8371), Eastman Kodak (110, 330).

F IG. 5.θm vs n for typical crown glasses. Bausch & Lomb (513 605, 523 586), Corning (8361, 8348).

February 1968 L E T T E R S T O T H E E D I T O R 279

FIG. 6. θm vs n for typical flint glasses. Bausch & Lomb (573 425, 580 410). Corning (8327, 8371), Eastman Kodak (110, 330).

where

Using Eq. (2), we have plotted the calculated values of (1— δ2) for typical crown and flint glasses for prism angles 20° to 60° on the ordinate and the corresponding sin2 (A/2) values on the abscissa, in Figs. 1 and 2. The values obtained for the slopes of these linear curves give average square of the nm3 values for these glasses. The calculated values of nms given in Table I for each of these typical glasses, when interpolated on n vs λ curves as plotted in Figs. 3 and 4, are seen to lie at 5500 Å within a range of ±25 Å, in conformity with the results1,2 obtained earlier for typical Jena glasses.

Rayleigh's dispersion formula is given by

where θm is the minimum deviation for the ray corresponding to n, t the base width, a the aperture of the beam, and K is a con­stant. The value of t/a for the condition of minimum deviation is given by4

Using Eq. (4), we have computed values of θm for a prism angle of 60° for the same glasses against n in Figs. 5 and 6. Since these are linear graphs, t/a for each of these glasses is obtained from their slopes, which are evaluated using the θm values for the F and C lines. The values of nms for each of these glasses were calcu­lated using Eq. (4) and are also given in Table I, along with the corresponding index values for the e line taken from the catalogue. These nms values are in good agreement with those obtained from Eq. (2).

From the present investigation we propose that the Mercury e line, 5461 Å, which is a strong line in the green region of the spec­trum, be taken as a more accurate mean-reference-index line for Bausch & Lomb, Eastman Kodak, and Corning glasses instead of the arbitrarily chosen sodium D line customary for dispersion studies between the F and C lines. We also confirm that the pro­posed mean-reference-index line is independent of the prism angles from 20° to 60° for all of these glasses.

The authors wish to thank Shri S. A. Abidin, Principal, Delhi College of Engineering, Delhi, for his interest and encouragement during the progress of the work.

1 P. Rajagopala Rao, J. Opt. Soc. Am. 55, 1032 (1965). 2 P. Rajagopala Rao and V. S. Shah, Indian J. Pure and Appl. Phys. 4

13 (1966). 3 Bausch & Lomb Optical glass catalogue, Rochester, New York 14602. 4 B. L. Sharda and P. Rajagopala Rao, J. Sci. Industr. Res. 21B, 448