Refractive indices of quartz with respect to air for wavelengths of 4500 Å and 4600 Å are respectively 1425 and 1460 .Find angular dispersion in degree/ Å unit.
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Answer:
The refractive indices listed in this catalog were determined to the fifth decimal place for the following 20 lines of the spectrum. The refractive indices for d-line (587.56 nm) and e-line (546.07 nm) were determined to the sixth decimal place.
Table1
Spectral Line t
Light Source Hg Hg Hg Hg Hg
Wavelength (nm) 2325.42 1970.09 1529.58 1128.64 1013.98
Spectral Line s A' r C C'
Light Source Cs K He H Cd
Wavelength (nm) 852.11 768.19 706.52 656.27 643.85
Spectral Line He-Ne D d e F
Light Source Laser Na He Hg H
Wavelength (nm) 632.8 589.29 587.56 546.07 486.13
Spectral Line F' He-Cd g h i
Light Source Cd Laser Hg Hg Hg
Wavelength (nm) 479.99 441.57 435.835 404.656 365.015
On the catalog pages, the wavelengths of each line are given in um units in parentheses under each spectrum line symbol.
2.2 Dispersion
We have indicated (n F -n C ) and (n F´ -n C´ ) as the main dispersions. Abbe numbers were determined from the following vd and ve formula and calculated to the second decimal place:
vd = (n d -1)/(n F -n C ) ve =(n e -1)/(n F' -n C' )
We have also listed 12 partial dispersions (n x -n y ), 8 relative partial dispersions for the main dispersion (n F -n C ) and 4 for (n F´ -n C´ ). To make achromatization effective for more than two wavelengths, glasses which have favorable relationships between vd and the relative partial dispersion ө x,y for the wavelengths x and y are required. These may be defined as follows:
θ (x,y ) = ( n x -n y ) / (n F -n C )
2.3 Dispersion Formula
The refractive indices for wavelengths other than those listed in this catalog can be computed from a dispersion formula. As a practical dispersion formula, we have adopted the use of the Sellmeier formula shown below.
n² -1={A1 Λ² /(Λ² -B1 )} + {A² Λ² /(Λ² -B² )} + {A3 Λ² /(Λ² -B3 )}
The constants A1 ,A2 , A3 , B1 , B2 , B3 were computed by the method of least squares on the basis of refractive indices at standard wavelengths which were measured accurately from several melt samples. By using this formula, refractive indices for any wavelength between 365 and 2325nm can be calculated to have an accuracy of around ± 5 ×106. These constants A1 ,A2 , A3 , B1 , B2 , B3 are listed on the left side of the individual catalog pages. However in some glass types, not all refractive indices in the standard spectral range are listed on the data sheet. In such cases, the applicable scope of this dispersion formula is limited to the scope where refractive indices are given. When calculating a respective refractive index, please bear in mind that each wavelength is expressed in µm units.
2.4 Effect of Temperature on Refractive Index(dn/dt)
Refractive index is affected by changes in glass temperature. This can be ascertained through the temperature coefficient of refractive index. The temperature coefficient of refractive index is defined as dn/dt from the curve showing the relationship between glass temperature and refractive index. The temperature coefficient of refractive index (for light of a given wavelength) changes with wavelength and temperature.
Therefore, the Abbe number also changes with temperature. There are two ways of showing the temperature coefficient of refractive index. One is the absolute coefficient (dn/dt absolute ) measured under vacuum and the other is the relative coefficient (dn/dt relative ) measured at ambient air (101.3 kPa {760 torr} dry air).
2.5 The refractive indices in Ultraviolet and the Infrared Range
The refractive indices in the ultraviolet and the infrared can be measured down to 157 nm in the ultraviolet and up to 2,325.42 nm in the infrared.
2.6 Internal Transmittance
Most types of Ohara optical glass are transparent and colorless because they are made of very pure materials. However, some optical glasses show remarkable absorption of light near the ultraviolet spectral range. For certain glasses with extreme optical properties, such as high refractive index, absorption extends to the visible range.
This not only depends on the chemical composition, but also on unavoidable impurities. In this catalog the internal transmittance is given - i.e., reflection losses are eliminated. Glass varies slightly from melt to melt and, therefore, listed are typical values of internal transmittance obtained on 10 mm thick samples chosen from many melts, measured from 280 nm to 2400 nm.
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