refractive index is denoted by the letter n, while spectrum line or wavelength is denoted by x.
twenty spectrum lines’ refractive indices of colorless optical glass provided in table 1 are measured by minimum deviation angle method.
test equipment: high precision refractive index tester (spectromaster uv-vis-ir) made by german trioptics.
measurement accuracy: ±3×10-6 in the ultraviolet range, ±2×10-6 in the visible range, ±5×10-6 in the near- infrared range.
sample requirements: no visible striae, bubbles or stones with naked eye, stress birefringence up to class 1.
upon special request, we can provide refractive index of any spectral line from 253.65nm to 14μm.
in the spectral range of 365.01nm~2325.42nm, the refractive indices not listed in the handbook can be calculated by the schott formula (1):
where: a0~a5—calculating constants;
λ—wavelength, μm；
n—refractive index (calculation accuracy at the visible band ±1×10-5)
table 1
spectral line | element | wavelength (nm) | spectral line | element | wavelength (nm) |
i | hg | 365.01 | c | h | 656.27 |
h | hg | 404.66 | r | he | 706.52 |
g | hg | 435.84 | a＇ | k | 768.19 |
f＇ | cd | 479.99 | s | cs | 852.11 |
f | h | 486.13 | t | hg | 1013.98 |
e | hg | 546.07 | nd laser | 1064.00 | |
d | he | 587.56 | hg | 1128.64 | |
d | na | 589.29 | hg | 1529.58 | |
he-ne | he-ne laser | 632.80 | hg | 1970.09 | |
c＇ | cd | 643.85 | hg | 2325.42 |
correlative spectrum lines’ refractive indices of low softening point glass (glass starting with d-) in this handbook are tested after -30℃/h annealing process. refractive index of d line changing with cooling rates βd is given in the handbook, and refractive index nd in cooling rates can be calculated by formula (2).
other spectrum lines’ refractive indices varying with cooling rates are also available if required.
the central dispersion is expressed by nf-nc or nf＇-nc＇.
abbe-number υd and υe are defined as:
relative partial dispersion is usually calculated with arbitrary spectrum lines. for example, relative partial dispersion for wavelength x and y can be expressed by formula (5):
the values of pd, c, pe, d, pg, f and p'd, c＇, p'e, d＇, p'g, f＇are given in the handbook.
according to the abbe-number formula, the following linear relationship is tenable for most ＂normal glass＂:
the deviation value △px, y of relative partial dispersion can be calculated by the following formula:
△pg, f, △pf, e, △pc,t and △pc,s against h-k6, f4 can be calculated by formula (8):
refractive indices of optical glass change with temperatures.the relationship of refractive index change to temperature change is called temperature coefficient of refractive index dn/dt. temperature coefficients of refractive indices are determined by temperature coefficients of relative refractive indices in the dry air (dn/dt)rel.(101.3kpa) and temperature coefficients of absolute refractive indices in the vacuum (dn/dt)abs..the testing data are provided every 20℃ from -60℃ to ＋160℃.
temperature coefficients of absolute refractive indices (dn/dt) abs. can be calculated by formula (9), and the temperature coefficients of refractive indices for air (dnair/dt) are indicated in table 2.
table 2
temperature (℃) | dnair/dt(10-6/℃) | |||||||||
t | s | c | c' | he-ne | d | e | f | f' | g | |
-60~-40 | -1.60 | -1.60 | -1.61 | -1.61 | -1.61 | -1.61 | -1.62 | -1.63 | -1.63 | -1.64 |
-40~-20 | -1.34 | -1.35 | -1.35 | -1.35 | -1.35 | -1.36 | -1.36 | -1.37 | -1.37 | -1.38 |
-20~0 | -1.15 | -1.15 | -1.15 | -1.15 | -1.16 | -1.16 | -1.16 | -1.17 | -1.17 | -1.17 |
0~ 20 | -0.99 | -0.99 | -1.00 | -1.00 | -1.00 | -1.00 | -1.00 | -1.01 | -1.01 | -1.01 |
20~ 40 | -0.86 | -0.86 | -0.87 | -0.87 | -0.87 | -0.87 | -0.87 | -0.88 | -0.88 | -0.88 |
40~ 60 | -0.76 | -0.76 | -0.76 | -0.76 | -0.77 | -0.77 | -0.77 | -0.77 | -0.77 | -0.78 |
60~ 80 | -0.67 | -0.67 | -0.68 | -0.68 | -0.68 | -0.68 | -0.68 | -0.69 | -0.69 | -0.69 |
80~ 100 | -0.60 | -0.60 | -0.60 | -0.61 | -0.61 | -0.61 | -0.61 | -0.61 | -0.61 | -0.62 |
100~ 120 | -0.54 | -0.54 | -0.54 | -0.54 | -0.54 | -0.55 | -0.55 | -0.55 | -0.55 | -0.55 |
120~ 140 | -0.49 | -0.49 | -0.49 | -0.49 | -0.49 | -0.49 | -0.49 | -0.50 | -0.50 | -0.50 |
140~ 160 | -0.44 | -0.44 | -0.45 | -0.45 | -0.45 | -0.45 | -0.45 | -0.45 | -0.45 | -0.45 |
the temperature coefficients of absolute refractive indices unspecified in the handbook can be calculated with the aid of equation (10).
where: n(λ,t0) —relative refractive index at the reference temperature;
t0—reference temperature (20 ℃);
t —targeted temperature (℃);
δt—temperature difference t-t0 (℃);
λ—wavelength of the electromagnetic wave in the vacuum (μm);
d0, d1, d2, e0, e1and λtk—constants depending on glass type.
the applied temperature range: -40℃ to 80℃;
the applied wavelength range: 0.3650 μm to 1.014 μm.
stress inside glass can result in change of optical properties, thereby birefringence appears. the stress photoelastic coefficient can be calculated by formula (11):
where :
δ—optical path difference, nm;
φ—sample diameter, cm;
f—the amount of force applied, pa;
b—stress photoelastic coefficient .
stress photoelastic coefficient is listed at a unit of (nm/cm/105pa), and the testing wavelength is 1550nm.
2.8 internal transmittance τ
the internal transmittance refers to transmittance excluding reflection losses at the surfaces of the sample. internal transmittance values are calculated from transmittance measurement of a pair of samples with single beam: measure transmittance of two samples of different thicknesses respectively, and then calculate mathematically.
test equipment: hitachi spectrophotometer (uh4150 uv-vis-nir)
measurement accuracy: better than ±0.3%.
sample requirement:bubble up to class 1, striae up to class b.
in the handbook, internal transmittance of 10mm (τ10) from 280nm to 2400nm can be calculated by formula (12).
………………………(12)
where: τ—internal transmittance based on transmittance of samples thicknesses is 10mm
△d—thickness difference of samples d2-d1 ( d2＞d1), mm,
t1, t2—transmittances including surface reflection loss obtained by thickness d1, d2 of the sample
the internal transmittances of different wavelengths for 5mm and 10mm thick glass are shown in the handbook.
transmitted spectrum performance of optical glass at short wave band can be expressed by the color code λ80(70)/λ5. measure the transmittance of glass with a thickness of 10mm±0.1mm (including reflection losses at the surfaces), wavelengths λ80 and λ5 respectively corresponding with transmittance 80%, 5% are used to express color code in 5 nm step(round off 2 and round up 3 or more, round off 7 and round up 8 or more of the bits of integers). for instance, if the corresponding wavelength of transmittance 80% is 357nm while transmittance 5% is 324 nm, the color code λ80 / λ5 is 355/325, as shown in figure 1.
figure 1
for a glass whose ne is higher than 1.85, λ70 is used in place of λ80 as a color code due to a heavier reflecting loss. that is to say, the color code is expressed by λ70/λ5.
the variance range of color code is usually within ±10 nm. upon special request, we can provide materials with smaller tolerance.
for a 10 mm thick glass, wavelengths λτ80 and λτ5 respectively corresponding with internal transmittance 80%, 5% are used to express coloring degree of the glass simply.
“solarization” means the transmittance change of optical glass due to sun or ultraviolet radiation for a long time. solarization is measured according to jogis: 04-2005. polish the two large sides of a 30mm×12.5mm×10mm sample, and test its corresponding transmission wavelength λ where the transmittance is 80% before solarization. fit the sample in the sample holder of solarization device, open mercury lamp to irradiate for 4h at 100℃±5℃, and then keep the sample in dark place and room temperature. test its corresponding transmittance after solarization at wavelength λ inside 24h. δλ refers to the transmittance difference before and after solarization. solarization δλ is expressed as a percentage and is accurate to one decimal place.