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2.1 Refractive index

 

Refractive indices to 5 decimal places are provided at the following 12 spectral lines shown in Table 2 for each optical glass type. The refractive indices at these spectral lines are measured by the methods described in GB/T7962.11, and the measure accuracy is ±3×10-5.

Table 2


Spectral Line

Element

Wavelength (nm)

Spectral Line

Element

Wavelength (nm)

i

Hg

365.01

d

He

587.56

h

Hg

404.66

D

Na

589.29

g

Hg

435.84

He+Ne

He-Ne

632.80

F'

Cd

480.00

c'

Cd

643.85

F

H

486.13

c

H

656.27

e

Hg

546.07

r

He

706.52



2.2 Dispersion and Abbe-number

Partial dispersion nF-nC and nF'-nC'are listed for each glass type.

The dispersion coefficient (Abbe-number) υd and υe are obtained from the following formula: 


 

 

2.3 Dispersion formula

Within the range of wavelength 365~706.5nm, refractive index against other wavelength can be calculated with the following formula:

Where, A0~A5―calculation constant (with the change of glass type, it can be different, and they are listed in the data sheet of each type respectively);

 λ―wavelength, µm

n―refractive index (calculation accuracy: ±3×10-6 within 400nm~706.5nm; ±5×10-6 within 360nm~400nm).


2.4 Relative partial dispersion

Relative partial dispersion PX, Y for wavelength X and Y can be obtained with the following formula:

 

Where, Pd, c, Pe, d, Pg, F and P'd, c', P'e, d', P'g, F' are given in the data sheet against the glass type.

According to Abbe-number formula, the following linear relation is tenable for the most called "normal glass":

The relation of straight line is shown by PX, Y (ordinate) and υd (abscissa). Where, mX, Y is slope, bX,Y is cut length. For the correction of second level spectrum, it means achromatic aberration of over two kinds of wavelength and at least one kind of glass which can not conform to formula (5) (i.e. the value of PX, Y deviated from the Abbe-experience formula) is needed. The deviation values is expressed by △PX, Y, each point of PX, Y-υd deviates △PX, Y relative to"normal line" which conform to formula (5). In that case, the values of △PX, Y of each type of glass can be calculated with the following formula:

So △PX, Y quantitatively indicate the deviation property of special dispersion compared with "normal glass".

The relative partial dispersion and Abbe-number of H-K6 and F4 conform to Abbe formula (5), so we choose them as "normal glass". 

△Pg, F, △PF, e are given in the data sheet according to the type. Their calculation formulae are as follows:



2.5 Temperature coefficient of the refractive index

The refractive index of optical glass changes depending on temperatures, and the changes can be expressed by temperature coefficient of refractive index dn/dt, which is determined by the dn/dt of refractive index-temperature curve. Temperature coefficient of refractive index is determined by the relative coefficient of refractive index in the air (dn/dtrelative, 101.3KPa{760torr}) and the absolute coefficient of refractive index in the vacuum (dn/dtabsolute) at the same temperature with optical glass.

Besides, temperature coefficient of absolute refractive index can be calculated by the following equation

In the data sheet, temperature coefficient of the refractive index dn/dt ,which should be used in the normal optical design, is measured at 20 ℃ intervals between -40~80 ℃ against each spectra line t(1,013.98nm), C'(643.85nm), He-Ne(632.8nm), D (589.29nm), e (546.07nm), F'(479.99nm) and g (435.835nm).

The dnair/dt in formula (8) is the temperature coefficient of refractive index in the air, and the values used in this product catalog are listed in the following table.

Table 3

Temperature (℃)

dnair/dt(10-6/℃)

t

C'

He-Ne

D

e

F'

g

-40~-20

-1.34

-1.35

-1.36

-1.36

-1.36

-1.37

-1.38

-20~0

-1.15

-1.16

-1.16

-1.16

-1.16

-1.17

-1.17

0~+20

-0.99

-1.00

-1.00

-1.00

-1.00

-1.01

-1.01

+20~+40

-0.86

-0.87

-0.87

-0.87

-0.87

-0.88

-0.88

+40~+60

-0.763

-0.77

-0.77

-0.77

-0.77

-0.77

-0.78

+60~+80

-0.67

-0.68

-0.68

-0.68

-0.68

-0.69

-0.69


2.6 Stress optical coefficient

The mechanical stress in glass can lead to birefirngence. The relationship among mechanical stress, optical path difference produced by stress birefirngence and stress optical coefficient is as follows:

Where

δ—optical path difference, nm;

B—stress optical coefficient;

d—the length of light path in the glass;

F—mechanical stress, Pa.


2.7 Internal transmittance and λτ80

The internal transmittance which is measured according to the method stipulated in GB/T 7962.12 refers to transmittance obtained by excluding reflection losses at the entrance and exit surfaces of the glass. In this catalog, the internal transmittance of 5mm and 10mm are shown as τ5mm and τ10mm, respectively, at wavelength between 280~2400nm. λτ80 refers to wavelength where the internal transmittance ratio reaches 80%, and thickness of the sample glass is 10 mm.


2.8 Coloration code (λ80/λ5)

The spectral transmittance characteristics of optical glass can be expressed by the coloration code (λ80/λ5).

The coloration code is determined by the following method: A sample of thickness 10mm±0.1mm is measured for transmittance. λ80 is the wavelength at which the glass exhibits 80% transmittance, while λ5 is the wavelength at which the glass exhibits 5% transmittance. The color code values are expressed in units of 10nm. For example, a glass with 80% transmittance at 357nm and 5% transmittance at 324nm has a coloration code 36/32 (shown in figure 1). When ne exceeds 1.85, λ70 instead of λ80 is used as a coloration code due to a heavier reflecting loss. That is to say, coloration code is expressed by λ70/λ5. λ70 is the wavelength at which the glass exhibits 70% transmittance. The tolerance is about +10/-20 nm.


Figure 1



 


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