malitson_1962#
I. H. Malitson, “Refraction and Dispersion of Synthetic Sapphire”, J. Opt. Soc. Am. 52, 1377 (1962)
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: Minimum deviation on the NBS Gaertner precision spectrometer (instrument, procedure and wavelength sources as in Rodney and Spindler, J. Res. NBS 51, 123 (1953)), ordinary ray of one synthetic sapphire prism supplied by the Linde Company in 1956 (faces about 3 x 3 cm, refracting angle near 40 degrees). 46 wavelengths from 0.2652 to 5.577 um ‘at controlled room temperatures near 24 C’, and 32 wavelengths near 19 C; emission lines (Hg, Cd, He, Cs) and absorption bands (1,2,4-trichlorobenzene, polystyrene, water vapour). A second sample, from a 1959 Linde boule, was measured at 24 C at several visible wavelengths and at 1.014 um. dn/dt from the 19 and 24 C indices, and in the visible from 17, 24 and 31 C on a Wild precision spectrometer (pp. 1377-1378).
Materials in structured entries: Al2O3
Dataset quantities: refractive_index
Contents: 4 datasets; 1 formula.
Curation notes#
Journal pages 1377-1379 are pdf pages 1-3. Identity checked against the first page.
AXIS. The ordinary ray, n_0, throughout Tables II and III (‘The observed and computed indices of refraction of synthetic sapphire for the ordinary ray n_0 at 24 C’); the prism’s orientation is not described. One extraordinary index is given in the text (dataset n_e_24C_text). The formula is for the ordinary ray only: this paper prints no extraordinary formula. Sapphire is uniaxial (negative: n_e < n_o, as the 1.014 um pair shows).
AIR OR VACUUM. Not stated. The measurements were made ‘at controlled room temperatures near 24 C’ (p. 1377) on the NBS instrument of Rodney and Spindler and Malitson (malitson_1963, malitson_1965), with the lines’ air wavelengths (Hg 0.546071 um, Cd 0.64385 um): as for those papers (TC-323, TC-399), the index is recorded as relative to the room air at 24 C (pressure not stated) and the wavelengths as standard air. An inference from the method, not a statement of the paper.
ACCURACY. ‘The goodness of fit is indicated by an average residual of index of 1.96 x 10^-5 and by a satisfactory number of changes of sign’ (p. 1378). The 1959 sample: ‘Excellent fifth-decimal agreement (+-1 x 10^-5) was found at several visible wavelengths and at 1.014 u for the ordinary ray’. No per-point uncertainty is stated.
TABLE II CHECKS (2026-09-27). The computed column is the formula’s value rounded to five decimals at 40 of 46 wavelengths; at the six polystyrene bands 3.2439-3.5070 um it is 3.5-6.7e-5 BELOW the formula (1.70433, 1.70354, 1.70231, 1.70136, 1.69814, 1.69501 against 1.704374, 1.703599, 1.702374, 1.701416, 1.698175, 1.695077). Not explained (a wavelength scale for those bands different from the printed one would do it: 6e-5 is about 0.002 um there); not corrected. The residual column is the observed minus the computed column except at two rows: at 1.01398 um 1.75547 - 1.75546 = +1 but -1 is printed; at 3.2439 um 1.70437 - 1.70433 = +4 but +3 is printed (against the formula, the residual there would be 0). The observed indices are taken as printed; which of the columns is misprinted at 1.01398 um cannot be told.
TABLE III is the formula at regular wavelengths, rounded to five decimals (60 of 61 values); 1.75554 at 1.00 um is a misprint for 1.75573 (erratum).
dn/dt (text only, p. 1378): ‘the coefficient is positive and decreases from about 20 x 10^-6/C at the short wavelengths to about 10 x 10^-6/C near 4 u. The average value of 13 x 10^-6/C for the visible region was determined from additional measurements made at 17, 24, and 31 C on a Wild precision spectrometer.’ Not recorded as data (rough values over wavelength ranges). Relative to the room air, so the absolute dn/dT is about 1.6e-6/K lower (not discussed in the paper). The 19 C indices (32 wavelengths) are not printed.
DIELECTRIC LIMIT (p. 1377): ‘At an infinite wavelength the formula approaches n^2 = 1 + Sum A. From the constants of the formula, n_inf^2 = epsilon = 8.4, as compared with a published value of epsilon = 8.6 +- 0.2 at 25 C for electric fields perpendicular to the optic axis’ (von Hippel). 1 + Sum A = 8.36.
EARLIER DATA. Malitson, Murphy and Rodney, J. Opt. Soc. Am. 48, 72 (1958), gave ‘fourth-decimal-place values’ for the same prism; this paper is ‘a more precise determination’ (p. 1377) and supersedes them (not in the library).
REFRACTIVEINDEX.INFO. main/Al2O3/nk/Malitson.yml (compared 2026-09-27): formula 1 with 1.023798, 0.06144821, 1.058264, 0.1106997, 5.280792, 17.92656, identical to Table I; range 0.2652-5.577 um; comment ‘Synthetic sapphire, Ordinary ray (o), 24 C’; no mention of air. main/Al2O3/nk/Malitson-o.yml and Malitson-e.yml, which solprop’s sapphire uses (o only), are NOT this paper: they cite Malitson and Dodge, J. Opt. Soc. Am. 62, 1405 (1972) (a talk abstract) and M. J. Dodge’s formula in the CRC Handbook of Laser Science and Technology IV (1986), p. 30, at 20 C (o: 1.4313493, 0.0726631, 0.65054713, 0.1193242, 5.3414021, 18.028251; range 0.20-5.0 um). Against this paper’s formula at the same wavelength argument, the handbook’s o-ray formula is lower by 9.4e-5 at 0.3 um, 6.9e-5 at 0.5, 5.2e-5 at 1.0, 4.8e-5 at 2.0, 3.9e-5 at 3.0 and 0.9e-5 at 4.0 um, and higher by 6.5e-5 at 5.0 um (recomputed 2026-09-27); the 4 K temperature difference accounts for about 5e-5 of that (dn/dt about +13e-6/K). The handbook and the 1972 abstract are not in the library.
REPRODUCTIONS. dragomir_2002’s sapphire index at 264 nm, 1.834 (‘from published dispersion relations’, citing this paper): this paper’s formula gives 1.83448 at 0.264 um, which rounds to it (checked 2026-09-27).
FIGURES (not digitised): 1, n_0 at 24 C and the relative dispersion (dn/dlambda)/(1 - n), minimum near 1.3 um, against a logarithmic wavelength scale; 2, (1 - n)/(dn/dlambda) and |(lambda dn/dlambda)^-1|.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
malitson_1962/observed_o_24C#
{
"id": "observed_o_24C",
"material": "Al2O3",
"file": "Al2O3/malitson_1962__observed_o_24C.csv",
"table": "tbl_9f97a99b9fc8",
"quantity": "refractive_index",
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "primary",
"parameters": {
"axis": "o",
"temperature_k": 297.15,
"grade": "Linde (1956)",
"form": "bulk",
"technique": "minimum deviation",
"index_medium": "air",
"air_temperature_k": 297.15
}
}
Table II, ‘Observed index’: the ordinary index n_0 of the 1956 Linde prism at 24 C, 46 wavelengths 0.2652-5.577 um. Relative to the room air (inferred; see the source notes). No per-point uncertainty is stated (average residual from the formula 1.96e-5). The residual column is misprinted or inconsistent at 1.01398 and 3.2439 um (see the source notes).
malitson_1962/computed_o_24C#
{
"id": "computed_o_24C",
"material": "Al2O3",
"file": "Al2O3/malitson_1962__computed_o_24C.csv",
"table": "tbl_9f97a99b9fc8",
"quantity": "refractive_index",
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "check",
"parameters": {
"axis": "o",
"temperature_k": 297.15,
"grade": "Linde (1956)",
"form": "bulk",
"index_medium": "air",
"air_temperature_k": 297.15
}
}
Table II, ‘Computed index’: the formula at the 46 wavelengths, ordinary ray, 24 C; the formula’s own column (the six polystyrene rows depart from the formula: see the source notes).
malitson_1962/table3_n_o_24C#
{
"id": "table3_n_o_24C",
"material": "Al2O3",
"file": "Al2O3/malitson_1962__table3_n_o_24C.csv",
"table": "tbl_a823708dead2",
"quantity": "refractive_index",
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "check",
"parameters": {
"axis": "o",
"temperature_k": 297.15,
"grade": "Linde (1956)",
"form": "bulk",
"index_medium": "air",
"air_temperature_k": 297.15
}
}
Table III: the formula at regular wavelengths, 0.270-0.990 um by 0.02, then 1.00-5.60 um by 0.2 (61 points), ordinary ray, 24 C; a sampling of the formula, not measurements. Rows in reading order (left column pair, then right).
malitson_1962/n_e_24C_text#
{
"id": "n_e_24C_text",
"material": "Al2O3",
"table": "text",
"quantity": "refractive_index",
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "primary",
"parameters": {
"axis": "e",
"temperature_k": 297.15,
"grade": "Linde (1959 boule, presumably)",
"form": "bulk",
"technique": "minimum deviation",
"index_medium": "air",
"air_temperature_k": 297.15
}
}
1 inline points in the source record.
Text, p. 1378: ‘The index for the extraordinary ray at 1.014 u was also measured and determined to be 1.74794.’ The sentence follows the measurements on the sample from the 1959 boule, so it is presumably that sample (the paper does not say). 1.014 um is presumably the Hg line of Table II, 1.01398 um. At 24 C, relative to the room air (inferred). The ordinary index there is 1.75547 (Table II).
Formulas#
malitson_1962/sellmeier_o#
{
"id": "sellmeier_o",
"form": "n2_sellmeier_wavelength",
"terms": {
"B": [
"1.023798",
"1.058264",
"5.280792"
],
"L": [
"0.06144821",
"0.1106997",
"17.92656"
]
},
"wavelength_medium": "standard_air",
"index_medium": "air",
"air_temperature_k": 297.15,
"range_nm": [
265.279,
5578.52
],
"material": "Al2O3",
"parameters": {
"axis": "o",
"temperature_k": 297.15,
"grade": "Linde (1956)"
},
"equation": "The equation of p. 1377 with Table I (p. 1377)",
"printed": "n^2 - 1 = A_1 lambda^2/(lambda^2 - lambda_1^2) + A_2 lambda^2/(lambda^2 - lambda_2^2) + A_3 lambda^2/(lambda^2 - lambda_3^2); lambda_1 = 0.06144821, lambda_1^2 = 0.00377588, A_1 = 1.023798; lambda_2 = 0.1106997, lambda_2^2 = 0.0122544, A_2 = 1.058264; lambda_3 = 17.92656, lambda_3^2 = 321.3616, A_3 = 5.280792",
"variable": "lambda: wavelength in um, the air wavelengths of Table II's lines (see the source notes)",
"range": "0.2652-5.577 um (the 46 wavelengths fitted), ordinary ray, 24 C; 'a dispersion equation for calculating the refractive index at any wavelength within the range of the measured spectral region' (p. 1377)",
"coefficients": {
"A1": "1.023798",
"lambda1": "0.06144821",
"lambda1_sq": "0.00377588",
"A2": "1.058264",
"lambda2": "0.1106997",
"lambda2_sq": "0.0122544",
"A3": "5.280792",
"lambda3": "17.92656",
"lambda3_sq": "321.3616"
},
"check": "Reproduces Table II's computed n_0 at 40 of 46 wavelengths to its five printed decimals (rounded); the six polystyrene bands 3.2439-3.5070 um are printed 3.5-6.7e-5 below the formula (see the source notes). Reproduces Table III at 60 of 61 wavelengths (rounded); the 61st is the erratum at 1.00 um. The printed lambda_i and lambda_i^2 give the same values. Checked 2026-09-27 against the printed coefficients."
}
Six constants ‘determined by a least-squares solution performed by a programmed electronic computer’ (Sutton and Stavroudis), ‘no physical interpretation of the parameters is claimed’ (p. 1377); fitted to the 24 C observed n_0, average residual 1.96e-5. The poles are printed as lambda_i and lambda_i^2 (Table I); the form uses lambda_i. Ordinary ray only. Relative to the room air at 24 C (inferred). Identical to refractiveindex.info main/Al2O3/nk/Malitson; NOT the formula solprop uses (Dodge’s handbook formula at 20 C, refractiveindex.info Malitson-o; see the source notes).
Corrections#
[
{
"dataset": "table3_n_o_24C",
"row": "1.00",
"column": "value",
"printed": "1.75554",
"corrected": "1.75573",
"reason": "Misprint: Table III is the formula rounded to five decimals (60 of 61 values), and the formula gives 1.7557300 at 1.00 um.",
"evidence": "Table III image (pdf p. 2) prints 1.75554 at 1.00 um. The Table I formula gives 1.75573 (checked 2026-09-27); the neighbours 1.75592 (0.99 um) and 1.75216 (1.20 um) and Table II's computed 1.75546 at 1.01398 um bracket 1.75573, while 1.75554 would fall 38e-5 in 0.01 um where the table falls 20e-5 per 0.01 um."
}
]
Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.