Refractive-index

FIGURE 8.2 Index of refraction for PLA as a function of wavelength from a global determination of the Cauchy parameters across all optical compositions. Adapted from Ref. 1 with permission from American Chemical Society. 

Malmgren et al. [18] determined the specific refractive index increment (d /dc) for PLA with 16.4% of D-isomer, which is amorphous. The resulting An versus concentration curve was measured using a differential refractometer. The authors gave two similar values for the resulting slope, An Ac, 0.0237 0.0034 and 0.0240 0.0049 mL/g, since the experiments were very difficult to carry out due to air bubbles inside the sample. The obtained d /dc values for PLA in chloroform are fairly small compared to those of other polymers such as polystyrene, which has a AnIAc of 0.169 mL/g in chloroform. 

Refractive index is a ratio technique that takes the velocity of light in air at a specific wavelength and compares that to the velocity in the sample tested. Normally this is performed under the guidelines of ASTM D 1218. This test method can be performed at various temperatures. The refractive index can be used to estimate the distribution of PNA molecules in oil fractions. 

The refractive index of an oil or melted fat is defined for practical purposes as the ratio of the speed of light in air to the speed of light in the sample (Rossell, 1986). The difference between these speeds results in light entering the sample from air, or indeed from any medium of different refractive index, being refracted. 

Measurement temperature must be controlled closely, and the oil sample must be optically clear and free of water. 

Standard methods for measuring the refractive index of oils and fats are published by IUPAC (standard method 2.102, Paquot Hautfenne, 1987), the American Oil Chemists Society (AOCS Official Method Cc 7-25, Firestone, 1998) and the International Standards Organization (International Standard 1739-1975 (E), ISO, 1975). The last specifically applies to the measurement of the refractive index of the fat from butter, and was developed jointly with the International Dairy Federation and the American Oil Chemists Society. 

The sample must be completely liquid, optically clear, dry and bright. Thus, the color of butter is actually determined on the extracted milk fat (Keen and Udy, 1980). The AOCS method 13e-92 requires that if a sample is not liquid at room temperature, it must be heated to a temperature 10°C above its clear melting point. The operator must not be color-blind. 

Lovibond tintometer color can also be measured using objective automated instruments. In one version, the intensities of three light beams (red, yellow and white) transmitted by the oil are measured by photoelectric cells, and the results displayed as red and yellow color readings. The white light beam acts as a reference beam, and allows compensation for variation in the intensity of the light source (Rossell, 1986). AOCS Official Method Cc 13j 97 (Firestone, 1998) specifies how an automated tintometer should be used. However, this standard is valid only for refined oils. 

The refractive index of coal can be determined by comparing the reflectance in air with that in cedar oil. A standard test method (ASTM D-2798) covers the microscopic determination of both the mean maximum reflectance and the mean random reflectance measured in oil of polished surfaces of vitrinite and other macerals in coal ranging in rank from lignite to anthracite. This test method can be used to determine the reflectance of other macerals. For vitrinite (various coals), the refractive index usually falls within the range 1.68 (58% carbon coal) to 2.02 (96% carbon coal). 

Since the speed of light in any material medium is less than the speed of light in a vacuum, the numerical value of the refractive index for any liquid is greater than one. 

An instrument known as a refractometer has been used for many years to measure the refractive index of liquids and liquid solutions for the purpose of both quantitative and qualitative analysis (see Chapter 15). A refractometer measures the degree of refraction (or bending) of a light beam passing through a thin film of the liquid. This refraction occurs when the speed of light in the sample is different from a reference liquid or air. The refractometer measures the position of the light beam relative to the reference and is calibrated directly in refractive index values. It is rare for any two liquids to have the same refractive index, and thus this instrument has been used successfully for qualitative analyses. 

The major advantage of this detector is that it is almost universal. All substances have their own characteristic refractive index (it is a physical property of the substance). Thus, the only time that a mixture component would not give a peak is when it has a refractive index equal to that of the mobile phase, a rare occurrence. The disadvantages are that it is not very sensitive and the output to the recorder is subject to temperature effects. Also, it is difficult to use this detector with the gradient elution method because it is sensitive to changes in the mobile phase composition. 

The refractive index of a medium is the ratio of the speed of light in a vacuum to its speed in the medium, and is the square root of the relative permittivity of the medium at that frequency. When measured with visible light, the refractive index is related to the electronic polarizability of the medium. Solvents with high refractive indexes, such as aromatic solvents, should be capable of strong dispersion interactions. Unlike the other measures described here, the refractive index is a property of the pure liquid without the perturbation generated by the addition of a probe species. 

Although the measurement of the refractive index of a liquid is relatively straightforward, few have been recorded for ionic liquids to date. Monoallcylammonium 

The refractive index, n, may be measured using an optical microscope [1,2,23,27,34]. Phase contrast increases the contrast due to differences in n and allows a more accurate determination. Interference contrast in transmission gives the optical path length and the average refractive index through the specimen thickness [1], The Becke line method gives the surface refractive index [1], 

The refractive index of fats and oils is sensitive to composition. The refractive index of a fat increases with increasing chain length of fatty acids in the triglycerides or with increasing unsaturation. This makes it an excellent spot test for uniformity of compositions of oils and fats. Further, the refractive index is an additive as well as constructive property, thus it can be used as a control procedure during hydrogenation processes. 

The refractive index is the ratio of the velocity of light in air to the velocity of light in the measured substance. The value of the refractive index varies inversely with the wavelength of light used and the temperature at which the measurements are taken. The refractive index is a fundamental physical property that can be used for the determination of the gross composition of residual fuel oil and often requires its measurement at elevated temperature. In addition, the refractive index of a substance is related to its chemical composition and may be used to draw conclusions about molecular structure. 

Two methods (ASTM D-1218, ASTM D-1747) are available for measuring the refractive index of viscous liquids. Both methods are limited to lighter-colored samples for best accuracy. The latter test method (ASTM D-1747) covers the measurement of refractive indexes of light-colored residual fuel oil at temperatures from 80 to 100°C (176-212°F). Temperatures lower than 80°C (176°F) may be used provided that the melting point of the sample is at least 10°C (18°F) below the test temperature. This test method is not applicable, within reasonable standards of accuracy, to liquids having darker residual fuel oil (having a color darker than ASTM Color No. 4 ASTM D-1500). 

The problem of instability in residual fuel oil may manifest itself either as waxy sludge deposited at the bottom of an unheated storage tank or as fouling of preheaters on heating of the fuel to elevated temperatures. 

Problems of thermal stability and incompatibility in residual fuel oils are associated with those fuels used in oil-fired marine vessels, where the fuel is usually passed through a preheater before being fed to the burner system. In earlier days this preheating, with some fuels, could result in the deposition of asphaltic matter culminating, in the extreme case, in blockage of preheaters and pipelines and even complete combustion failure. 

Asphaltene-type deposition may, however, result from the mixing of fuels of different origin and treatment, each of which may be perfectly satisfactory when used alone. For example, straight-run fuel oils from the same crude oil are normally stable and mutually compatible whereas fuel oils produced from thermal cracking and visbreaking operations that may be stable can be unstable or incompatible if blended with straight-run fuels and vice versa (ASTM D-1661). 

The refractive index (RI) is a parameter that relates to molecular weight, fatty acid chain length, degree of unsaturation, and degree of conjugation. A mathematical relationship between refractive index and iodine value (IV) has been described by Perkins (1995b) as 

The reverse relationship can be used to calculate the iodine value of crude soybean oil when the RI is known. RI was shown to increase by 0.000385 for each degree rise of temperature. 

The refractive index is widely employed in conjunction with the boiling point for characterising organic substances [59]. In the separation of close-boiling substances a continuous determination of the refractive index allows the conditions of distillation to be so chosen that the transition fractions remain as small as possible and yields are consequently increased. 

Photodectric refractametera indicate their reading on the scale of an electric measuring instniment and hence permit this reading to be recorded. 

Automatic and continuously recording flow refractometers have been developed by Thomas et al. [61] and by Latchum [62], 

The model Remat 10 of VEB Carl Zeiss Jena [63] is a differential flow refracto-meter. It compares the refractive index of the flowing sample with that of the reference liquid which can be arbitrarily chosen. Fig. 391 shows the front and back of 

Stage s arrangement (Fig. 392) designed for measurements of phase equilibria, appears useful. Two commercial flow refractonieters are so arranged in the equilibrium apparatus that they indicate the refractive indices of the liquid and vapour phases and thus enable their compositions to be determined. 

Refractive indices for a number of ionic liquids have been reported recently [30]. Increasing the number, length and branching of alkyl chains on the cations increases the refractive index, as does introducing functionality into the chain. Changing the anion of the ionic liquid also affects the refractive index, perhaps with less polarizable anions giving lower values. 

The hyperfine coupling constant of the EPR spectrum of 4-amino-2,2,6,6-tetramethylpiperidine-l-oxyl, a commercially available stable free radical, has been 

An alternative avenue to exploring the polarity of a solvent is by investigating its effect on a chemical reaction. Since the purpose of this book is to review the potential application of ionic liquids in synthesis, the effect of ionic liquids on chemical reactions has been treated separately (see Chapter 5, Section 5.1). 

The refractive index remains the most measured optical property of glasses, as well as the most basic optical property for determination of the appropriate glass for many applications. The refractive index of any material is defined as the ratio of the velocity of light in a vacuum divided by the velocity of light in a medium. This ratio can be measured by application of Snell s law, which states that the refractive index, n, is given by the expression  

The refractive index is not actually a constant, but varies with the wavelength of the incident light. The most commonly quoted index is usually designated as and represents the index at the yellow emission line of sodium (589.3 nm). The index at the yellow emission line of helium (587.6 nm), designated is also commonly used. Since these wavelengths are nearly identical, there is very little difference between these indices. 

Since a majority of the ions in any glass are usually anions, the contribution to the refractive index from the anions is very important. Replacement of fluorine by more polarizable oxygen ions, or by other halides, increases the refractive index. Conversely, partial replacement of oxygen in oxide glasses by fluorine to form fluoroborate glasses, for example, reduces the refractive index. Since non-bridging oxygens are 

Although refractive index detectors are common on analytical systems due to then-universal nature, they have a number of disadvantages for process use. Their advantage is their ability to detect compounds such as carbohydrates, lipids, and simple peptides, which possess no measurable UV absorption. Offset against this is their incompatibility with gradient operation and often their need for a flow splitter to cope with process scale flow rates. This latter is undesirable for any detector, due to the fact that the relative flow rate through the detector cell can vary depending on solvent viscosity and flow rate. 

The vast majority of refractive index detectors are differential detectors where the refractive index of the sample is measured relative to a reference liquid. This enables them to be used in a wide range of applications but requires a fairly delicate flow cell. Absolute refractive index detectors are available which although only covering a limited range and less sensitive, are more robust and have sensor probes which can be easily inserted in the process stream. These are especially suited to explosion proof applications. 

Storage of the system will require the electrode to be kept wet, either in situ, or removed from the unit. Similarly it may be necessary to protect the electrode during cleaning from, for instance, hot caustic solutions, in which case a self sealing fitting or other means of isolation is required. 

Conductivity sensors may be either the contacting tsrpe or the induction type. The contacting type may utilize either 2 or 4 electrodes. The four electrode cell permits measurement of higher ranges (up to 200 mS), and the correction of polarization effects due to deposits forming on the electrodes. Two electrode types are suitable for lower conductivity ranges and are easier to insert into a flow through cell but cannot compensate for polarization. Four electrode types are incorporated into the system in a similar manner to pH probes. 

If only one pH and/or conductivity sensor are utilized it is usual to locate them after the column to monitor the column eluent. They may, however, be additionally located prior to the column to act either in an alarm only mode to protect the column from extremes of pH due, for instance, to failure of a caustic dilution step, or to enable equilibration of a column to be continued until the pre and post column pH or conductivity measurements are equivalent. 

In optics, the refractive index (or index of refraction) of a material or medium is considered a normalized value of the speed of propagation of light in the medium. It is a ratio of the speed of light in a vacuum relative to that in the 

Ray Matrices for Typical Optical Elements and Media Straight section with length d 

Thin lens focal length/(f 0, converging / 0, diverging) Dielectric interface refractive indices W] and Wj Spherical dielectric interface radius R Spherical mirror radius of curvature R 

Another definition of the refractive index comes from the refraction of a light ray entering a medium. The refractive index is defined as the ratio of sines of the incident angle 0j and the refracted angle 02 as light passes into the medium, as expressed in Equation (2.4). 

The angles are measured to the normal of the surface. This definition is based on Snell s law and is equivalent to the definition above if the light enters from the reference medium. The refractive indices of materials are not constants and vary based on certain parameters such as temperature and especially the wavelength (frequency) of light, which is called dispersion. Dispersion may cause the focal lengths of lenses to be wavelength dependent. This is one source of chromatic aberration that requires correction in imaging systems. Chromatic aberration is discussed in some detail in Section 2.2.4.5. 

Fluoro compounds have a lower refractive index than their hydrocarbon and halo-carbon analogs. The refractive indexes of monosubstituted halobenzenes increase in the order F H CKBr I (Table 3.14). The low refractive index of fluo-robenzene is related to the low polarizability of the fluorine atom. The polarizability, Pe, can be calculated from atomic contributions (Table 3.14), of which fluorine has the lowest value. 

Refractive Indexes and Surface Tensions of Benzene Derivatives 

X Atomic refractive constant of X Refractive index nF) Surface tension (y) 20°C (vapor) 

The refractive index of perfluorinated compounds is exceedingly low [19]. Perfluoropentane has probably the lowest refractive index (n 1.333) ever recorded. 

Refractive indexes of some fluorinated surfactants are listed in Table 3.13. 

The method of determination of refractive index specified for plasticizers was developed for electrical insulating liquids. A refractometer is used with a spectral line of sodium (589.3 nm) at the test temperature of 25°C. 

Refractive index can be measured with a high precision to five decimal places using critical angle method with Bausch Lomb Precision Refractometer. This method can be used for the transparent and light colored liquids measured at temperatures from 20 to 30°C. Several light sources and filters are specified in order to provide monochromatic light. Also, calibration and calibration liquids are described to assure high precision of measnrement. 

In addition to the boiling curve, the density and refractive index are used to assess and, with some restrictions, to determine solvent purity. 

The density of a solvent is generally measured at 20 C and referred to the density of water at 4 °C (relative density dl°). The densities of most organic solvents decrease with increasing temperature (Fig. 6) and are less than that of water, but halogenated hydrocarbons are denser than water. The relative densities of homologous 

The refractive inde.x is measured in a refractometer with a sodium vapor lamp (Na-D lines, 589.0 and 589.6 nm). The value of the refractive index [14.45], [14.46], [14.80] is largely determined by the hydrocarbon skeleton of the substance in question. Aliphatic esters, ketones, and alcohols have refractive indices between 1.32 and 1.42. In homologous series the refractive index increases with increasing length of the carbon chain, and decreases with increasing branching. Cycloaliphatic and aromatic structures increase the refractive index (/Jd ), as does the incidence of functional groups  

The refractive index decreases with increasing temperature (Fig. 7). 

Among the most important optical properties of a material is its refractive index, or more correctly speaking, the refractive index experienced by a particular polarized light traversing the medium. For simplicity, we shall focus our attention in this chapter to crystalline materials such as Uquid ciystals in which there are three well-defined principal ciystalline axes. For such ciystals, the dielectric and permeability tensors are diagonal. Furthermore, we also limit our attention to linear responses, i.e., the induced polarization Pis proportional to the optical electric field E  

In the principal axes coordinate, x is diagonal. Accordingly, the optieal dielectric tensor s, or permittivity, of the medium is diagonal  

The permittivity e (and its magnetic counterpart, the permeability p) are complex in general, with an imaginary component accounting for losses (e.g., the finite electric conductivity). The relative permittivity Zy may be expressed as 

Similarly, the linear magnetic polarization is expressed in terms of the magnetic field intensity and the magnetic susceptibility  

If the plane- polarized wave propagating in the positive z direction is expressed in the form then the imaginary parts of both the permittivity and the perme- 

Cubic crystals like halite (common salt or rock salt) have the same refractive index in all directions and are said to be optically isotropic. All 

This correlation is unsurprising. The refractive index depends upon the density of atoms in a crystal. In cubic crystals the atom density averages to be the same in all axial directions while in crystals of lower symmetry some axial directions contain more atoms than others. 

A beam of unpolarised light can be resolved into two linearly polarised components with vibration directions perpendicular to each other. For convenience these can be called the horizontally and vertically polarised components. When the beam enters a transparent medium, each of the two linearly polarised components experiences its own refractive index. 

In the field of processing or engineering, there is a potential requirement for materials with high refractive index. However, these materials are typically all solid and those liquids that are known are poisonous. Accordingly liquids having 

From this table, it is clear that refractive index of ILs increases with increase in the alkyl chain length of the imidazolium cation. Moreover, the refractive index is strongly afFected by the anion the refractive index of ILs with larger anions, such as [(CF3S02)2N]- (TFSI anion) is lower than that of ILs having smaller anions such as acetate or halide anions. 

Furthermore, Seddon et al. reported that the poly-halide salts, such as [EMIM][IBr2] or [EMIM][Is], have a high refractive index of 1.6 or more, as shown in Table 3.7 [67]. The high refractive indices of the lanthanide salts and the heavy halogens and their trihalide salts are well predictable from their polarizabilities, which in turn are well understood on the basis of periodic table trends atoms/ions with partly filled 4f, 5d etc. shells tend to be quite polarizable and hence have high refractive indices. 

Before answering that, it is necessary to return to the isotropic case and look more closely at what happens when light crosses a refractive index boundary. It has 

One of the main goals of the optical materials engineer is to control the direction of light flow. For the electrical engineer, the analogous task of controlling the flow of 

This production of a core with a refractive index higher than the cladding raises the important question of how a refractive index can be manipulated. To answer this question, 

A detailed treatment of this model results in an expression for the refractive index shown below (Feynman et al., 1963). 

the density of charges affects the refractive index. All other factors being equal, as the atomic number of the constituent elements increases, the refractive index of a material will also increase. This can be seen with a simple listing of a few minerals in Table 9.1. 

The velocity of light often changes with the medium through which the light is transmitting. This property can be nsed to give the most fundamental definition of refractive index (n), which is the ratio of the velocity of light in a vacuum (v ) 

Refractive index is a basic optical properly of fibers that is directly related to other optical properties. In general, the refractive index of fibers varies with temperature and wavelength. The standard conditions for refractive index measurement involve the use of specific wavelength (589 mn) at a specific temperature (20°C). 

The refractive index of fibers also is aifected by the fiber density. This is because electronic polarizability increases when the number of electrons per unit volume increases. For many fibers, the relationship between refiactive index and fiber density p) can be expressed by Gladstone and Dale s law  

Most fibers are anisotropic and the refractive index value is directional. When the average refractive index is used, the constant in Equation 20.3 is around 0.3570. 

A similar relationship can be obtained between the refractive index nj and volume (vj of a mixture of different components  

When radiation is incident on an interface between two materials, part of the energy is reflected at the interface and the rest is transmitted through it. Irrespective of whether the radiation involved is a beam of light, x-rays, or neutrons, the geometry and the relative intensities of the reflected and refracted rays can be described by the principles of optics,4 once the refractive indices of the two media are known. The concept of refractive indices of neutrons was briefly introduced in Section 

2 in connection with neutron guide tubes. For both x-rays and neutrons, the refractive index n of a material is in general slightly less than 1 and is given to a good approximation by 

Here it is assumed that the slab is sufficiently thin so that the absorption effect is negligible. 

Next we take the viewpoint that the wave reaching a point on the right of the slab can be considered to result from the sum of the waves scattered at every point on the slab plus the unmodified incident wave, and thus its amplitude is given by 

Refractometric measurements can often be used for the rapid measurement of solution concentration. Several standard instruments (Abbe, Pulfrich, etc.) are available commercially. A sodium lamp source is most usually used for illumination, and an instrument reading to the fourth decimal place is normally adequate for crystallization work. It is advisable that calibration curves be measured, in terms of temperature and concentration, prior to the study with the actual system. 

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Characterization of a Petroleum Cut by Refractive Index, Density, and Molecular Weight (ndM method)... 

As in the case of density or specific gravity, the refractive index, n, for hydrocarbons varies in relation to their chemical structures. The value of n follows the order n paraffins < n naphthenes < n aromatics and it increases with molecular weight. 

With the accumulation of results obtained from various and complex analyses of narrow cuts (Waterman method), correlations have been found f ctween refractive index, specific gravity and molecular weight on one hand, and percentages of paraffinic, naphthenic and aromatic carbon on the other. 

Refractive index this is one of the most precise measurements that can be carried out on a petroleum cut. The ASTM method D 1218 indicates a reproducibility of 0.00006, which is exceptional. 

As a consequence, other than its use in the ndM method, the refractive index is very often used in process operations because it can indicate smaii differences in product quality that would be missed by other measurements. The only restriction is that the color of the sample should be less than 5 on the ASTM D 1500 scale. 

Consider the reflection of a normally incident time-harmonic electromagnetic wave from an inhomogeneous layered medium of unknown refractive index n(x). The complex reflection coefficient r(k,x) satisfies the Riccati nonlinear differential equation [2] ... 

The reconstruction algorithm proposed in this work is based on a special choice of basis flinctions to expand the unknown refractive index profile. The following set of functions is used here ... 

In an early study, Greenleaf et al. [4] reported reconstructions of ultrasonic velocity from time-of-flight profiles. Since then there has been periodic activity in using ultrasound to determine the transmission properties attenuation or refractive index. 

The physics of X-ray refraction are analogous to the well known refraction of light by optical lenses and prisms, governed by Snell s law. The special feature is the deflection at very small angles of few minutes of arc, as the refractive index of X-rays in matter is nearly one. Due to the density differences at inner surfaces most of the incident X-rays are deflected [1]. As the scattered intensity of refraction is proportional to the specific surface of a sample, a reference standard gives a quantitative measure for analytical determinations. 

Figure 1. shows the measured phase differenee derived using equation (6). A close match between the three sets of data points can be seen. Small jumps in the phase delay at 5tt, 3tt and most noticeably at tt are the result of the mathematical analysis used. As the cell is rotated such that tlie optical axis of the crystal structure runs parallel to the angle of polarisation, the cell acts as a phase-only modulator, and the voltage induced refractive index change no longer provides rotation of polarisation. This is desirable as ultimately the device is to be introduced to an interferometer, and any differing polarisations induced in the beams of such a device results in lower intensity modulation. 

In the case of Langmuir monolayers, film thickness and index of refraction have not been given much attention. While several groups have measured A versus a, [143-145], calculations by Knoll and co-workers [146] call into question the ability of ellipsometry to unambiguously determine thickness and refractive index of a Langmuir monolayer. A small error in the chosen index of refraction produces a large error in thickness. A new microscopic imaging technique described in section IV-3E uses ellipsometric contrast but does not require absolute determination of thickness and refractive index. Ellipsometry is routinely used to successfully characterize thin films on solid supports as described in Sections X-7, XI-2, and XV-7. 

Brewster angle microscopy takes advantage of the reflectivity behavior of light at an interface. This method relies on the fact that light passing from a material of lower refractive index, no into a medium of higher index i will have... 

For example, the definition of a system as 10.0 g FI2O at 10.0°C at an applied pressure p= 1.00 atm is sufficient to specify that the water is liquid and that its other properties (energy, density, refractive index, even non-thennodynamic properties like the coefficients of viscosity and themial condnctivify) are uniquely fixed. 

If the scattering particles are in a dielectric solvent medium with solvent refractive index Uq, we can define the excess... 

Nonetheless, the syimnetric interferometer remains very useful, because there, the wavelengdis of fringes with even cliromatic order, N, strongly depend on the refractive index, n, of the central layer, whereas fringes with odd cliromatic order are almost insensitive to This lucky combhiation allows one to measure the thickness as well as the refractive index of a layer between the mica surfaces independently and siniultaneously [49]. 

In the symmetric, three-layer interferometer, only even-order fringes are sensitive to refractive index and it is possible to obtain spectral infonnation of the confined film by comparison of the difierent intensities of odd-and even-order fringes. The absorption spectmm of tliin dye layers between mica was investigated by Muller and Machtle [M, M] using this method. 

Figure Bl.26.9. Schematic diagram showing the reflection of light incident at an angle from a medium with refractive index n tln-ough a film of thickness d with refractive index n. ...

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