Cauchy's Constants Research Articles

FECO fringes for investigating the effect of grafting process on the dispersion properties of polyamaide-6 fibers.

Polyamide-6 fiber was modified by grafting it with poly(methyl methacrylate) PMMA polymer. The grafting process is widely used in industry to introduce new properties and overcome some obstacles, for instance, in storing energy applications. Multiple-beam interference techniques are very precise techniques to characterize the different properties of polymeric fibers. Fringes of equal chromatic order FECO technique was used to study the effect of grafting process on the dispersion properties of polyamides fibers. A mechanical drawing device was attached to the FECO system to evaluate the mechanical deformation impact on the samples and on their dispersion properties. The dispersion properties were evaluated by measuring their refractive indices, Cauchy's constants, average excitation energy, dispersion energy, lattice energy, interband oscillator wavelength, static dielectric constant, and Abbe's dispersion number. The results show that grafting polyamide-6 with PMMA produced a new material with a different structure and different dispersion properties. Microinterferograms, graphs and tables were given for illustrations.

The Harmonic Interchangeability Variance of Cauchy Constant’s Value: A and B

The strong relationship of refractive index of a material with wavelengths dates back to more than a century especially where Sellmeier’s equation was invented by Wolfgang Sellmeier in 1871 and then developed by Cauchy for visible region of electromagnetic waves. In this work, we studied the interchangeability of Cauchy constants A and B for a glass prism by using inert gas light sources such as He and Ne and metal vapor light sources as Hg, Cd, HgCd, and Na. Cauchy formula represents this dependence where A and B are Cauchy constants and their value are harmonically interchangeable. We investigated that each light sources have a different value of A and B and does not follow the same pattern of graphical representation. From this result, one can notice that Cauchy constants have a crucial role on this dependence of refractive indices on the wavelength of the light sources. The novelty of this work is the combination of Geometrical Optics and Wave Optics, then formulating a new equation, which is exactly geometrical measurements.

Measuring opto-thermal parameters of basalt fibers using digital holographic microscopy.

A method for studying the effect of temperature on the optical properties of basalt fiber is presented. It is based on recording a set of phase-shifted digital holograms for the sample under the test. The holograms are obtained utilizing a system based on Mach-Zehnder interferometer, where the fiber sample inserted in an immersion liquid is placed within a temperature controlled chamber. From the recorded digital holograms the optical path differences which are used to calculate the refractive indices are determined. The accuracy in the measurement of refractive indices is in the range of 4 × 10-4 . The influence of temperature on the dispersion parameters, polarizability per unit volume and dielectric susceptibility are also obtained. Moreover, the values of dispersion and oscillation energies and Cauchy's constants are provided at different temperatures.

Vacuum annealing effects on the structural and optical properties of SnSb2S4 thin films fabricated by thermal evaporation technique

SnSb2S4 thin films have been deposited by thermal evaporation technique on non-heated glass substrates and subsequently annealed at 473 and 673K. The influence of annealing temperature on the structural, morphological, optical and electrical properties was analyzed by X-ray diffraction, atomic force microscopy (AFM), spectrophotometer and hot probe method, respectively. The as-deposited and annealed films were polycrystalline in nature with preferential growth along (621) plane. The SnSb2S4 films annealed at 673K exhibited an optical transmittance of 30% and a direct band gap of 1.4eV. The dispersion behavior of the refractive index was studied in terms of the single-oscillator Wemple–DiDomenico and Cauchy models, and the optical parameters such as refractive index, extinction coefficient, oscillator energy, dispersion energy and Cauchy's constants were found. The electrical free carrier susceptibility and the carrier concentration on the effective masse ratio were estimated according to the model of Spitzer and fan.

Effect of UV radiation on the optical and some structural properties of irregular rayon acetate fibers

This recent study shed demonstration on how the structural parameters changes due exposure to UV radiation and different wavelengths. So this article throws light on the changes of the optical properties and some structural properties due exposure to UV radiation and different wavelengths on irregular rayon acetate fibers. Pluta polarizing interference microscope is used to study the changes for refractive indices and birefringence with different exposure times at three different intensities on irregular rayon acetate fibers. As the principal optical parameters determined, these give an indication of the isotropic refractive index, stress optical coefficient, stress due to UV radiation, optical configuration parameter, segment anisotropy, the number of molecules per unit volume and polarizability of a monomer unit can be obtained. Also by using different wavelengths are given the spectral dispersions, Cauchy's dispersion constants, the resonant wavelength, the oscillation energy, the dispersion energy, the dielectric constant and the dielectric susceptibility for rayon acetate fibers with different wavelengths at room temperatures. Illustrations are given using graphs and microinterferograms.

Visible Channeled Spectra of a Multilayer Wood Filter

ABSTRACT The transmission factor of multilayer Wood filters containing quartz and rutile layers was simulated in order to avoid the experimental trials for obtaining optical filters with predicted transmission. The main refractive indices of uniaxial crystals—quartz and rutile—were interferometrically determined and Cauchy constants were obtained by simulation. The transmission factor of optical devices consisting of quartz and rutile layers was simulated using the Maple Program.

Interferometric determination of the birefringence of thermo‐tropic polyester fibers and its copolymers of structure (PCPT‐co‐CPO)

AbstractThe aim of this study is to determine the optical anisotropy of three different samples of thermo‐tropic polyester fibers of structure Poly(chloro‐1,4‐phenylene terephthalate‐co‐4,4′‐oxybisbenzoate) and its copolymers (PCPT‐co‐CPO). The molar fraction of disruptor units ([CPO]) ranging from 0.40 to 0.60. The variable wavelength interferometry, VAWI technique, was used to determine the birefringence and spectral dispersion properties of such of these fibers. The Cauchy's dispersion formula and its related constants were determined using the spectral dispersion curves of the birefringence. A mathematical formula was derived for direct measurement of the birefringence profile of highly birefringent polymer fibers using VAWI technique. The effect of varying copolymer molar fractions of the three samples of thermo‐tropic polyester fibers was investigated throughout the spectral dispersion curves, the Cauchy's formula constants and the birefringence profiles. Microinterferograms are given for illustration. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

Laser interferometric study of the physical properties of transformer oil

This paper describes the optical, thermal, and electrical properties of an important nonpolar dielectric liquid, transformer oil. Applying dual laser (He–Ne and Argon laser of wavelengths 632.8 and 514.5 nm, respectively), and the Mach–Zehnder interferometric technique, the refractive indices and its temperature gradients are determined. Using Maxwell's and Cauchy's equations, the following optical, thermal, and electrical properties are calculated: optical and dielectric dispersion, optical permittivity and its thermal coefficient, thermal coefficient of volume expansion, specific refraction, specific dispersivity, characteristic impedance, electric susceptibility, and the variation of Cauchy's emperical constants with temperature. Additionally, different physical phenomena are studied as functions of wavelength and temperature.

Thermo-optical properties of polar dielectric laser dye solvents

This work is devoted to study the thermo-optical properties of three important pure polar dielectric laser dye solvents (aniline, pyridine and ethyl ether). Experimental measurements of the refractive index n and its thermo-optic coefficient dn/dT are carried out using dual laser Mach–Zehnder interferometric technique. The determined values of n and dn/dT are used to extract new data concerning the mentioned laser dye solvents. Applying the empirical relationship of Cauchy between the refractive index and the wavelength, the optical dispersion dn/ dλ and dn/dT, as a function of wavelength are calculated and represented. Additionally, Cauchy's constants as a function of temperature has been calculated and a comparison between the studied solvents are considered.

Refractive Index and Fourier Transform Infrared Spectra of Virgin Coconut Oil and Virgin Olive Oil

This study presents the refractive index and FTIR spectra of virgin coconut oil and virgin olive oil that have been measured in the wavelength range from 491.0-667.8 nm. The measurement of refractive index was carried out using a minimum deviation method while the IR transmission ranging from 600-4000 cm-1 was measured using FTIR spectrometer respectively. The measurements were done at room temperature and the dispersion equations for the studied samples were verified and the Cauchy constants were obtained by fitting the experimental data to the Cauchy formula. For both, refractive index and Cauchy constants, the value obtained are higher in virgin olive oil as compared to virgin coconut oil. A similar result for FTIR absorption spectrum was also observed where the five important peaks explaining the stretching absorption due to aldehyde (C = O) and esters (C-O), bending absorption (methylene (CH2) and methyl (CH3) groups and double bond absorptions (C = O) were strong in virgin olive oil.

Optical Properties of Gamma-Irradiated ST/MMA Copolymer

Copolymer films, with various concentrations of styrene (ST) and methyl-methacrylate (MMA), were prepared by thermal polymerization. The films were exposed to different doses of gamma rays up to 10 Mrad. The optical absorption α and the optical parameters, including the energy band gap E g and band tail width E w , were estimated for the films before and after irradiation by gamma rays. Furthermore, the effect of UV radiation on un-irradiated films was investigated. The specular reflection of PS, PMMA, and copolymer has been measured. The refractive index and Cauchy's constants were evaluated for the films before and after irradiation by gamma rays. The structure–property behavior of the films was scrutinized by DSC and FT-IR.

Interferometric Determination of Structural Properties of PEN Highly Oriented Fiber

Some optical and structural properties of Poly(ethylene naphthalate-2.6-dicarboxylate), PEN, highly oriented fiber was determined using an automatic variable wavelength interferometric, VAWI, technique. This technique is commonly used jointly with the double refracting polarizing interference microscope designed by Pluta. The microscope was used in two different positions, the subtractive position for determining the spectral dispersion curves of the birefringence and the crossed position for determining the spectral dispersion curves of the refractive indices. The resulting data are utilized to calculate some dispersion and structural parameters such as Cauchy's constants, natural wavelength, dispersion energy, oscillation energy, polarizability per unit volume, dielectric constant, dielectric susceptibility, optical orientation function, and the orientation angle. Microinterferograms are given for illustration.

Optical characterization of Cu 2+ ion-doped zinc lead borate glasses

We have developed a new series of zinc lead borate (ZLB) glasses by varying ZnO content, to enhance UV transmission, in the chemical composition of xZnO–15PbO–(85− x)B 2O 3, where x = 0 , 5, 10, 15, 20, 25, 30, 35, 40 and 45 mol% ZnO. From the measurement of UV absorption spectra both the direct and indirect band gaps have been evaluated. Also different physical properties of a reference glass of 45ZnO–15PbO–40B 2O 3 have been studied. From the measurement of refractive indices at six different wavelengths, Cauchy's constants ( A = 1.578743209 ; B = 131832.33 nm 2 and C = - 0.77756 × 1 0 10 nm 4 ) have been computed and a satisfactory correlation has been achieved between the theoretical and the experimental results. Absorption spectra of Cu 2+(45− x)ZnO–15PbO–40B 2O 3 (where x=0.1, 0.2, 0.5 and 1.0 mol%) have shown two absorption bands at 428 nm ( 2B 1g→ 2E g) and 777 nm ( 2B 1g→ 2B 2g). Emission spectra of (1.0 mol%) Cu 2+:ZLB have revealed two emission transitions at 400 and 493 nm with excitations at 288 and 316 nm.

Spectral analysis of Cu 2+: B 2O 3–ZnO–PbO glasses

A new series of heavy metal oxide (PbO) based zinc borate glasses in the chemical composition of (95 − x)B 2O 3–5ZnO– xPbO ( x = 10, 15, 20, 25, 30, 35, 40, 45 and 50 mol%) have been prepared to verify their UV filtering performance. Both direct and indirect optical band gaps ( E opt) have been evaluated for these glasses. For a reference glass of 45B 2O 3–5ZnO–50PbO, refractive indices at different wavelengths are measured and found the results satisfactorily correlated with the theoretical data upon the computation of Cauchy's constants of A = 1.766029949, B = 159531.024 nm 2 and C = −1.078 × 10 10 nm 4. Measurements concerning X-ray diffraction (XRD), FT-IR, differential scanning colorimeter (DSC) profiles have been carried out for this glass. The FT-IR profile has revealed that the glass has both BO 3 and BO 4 units. From DSC thermogram, glass transition temperature ( T g), crystallization temperature ( T c) and melting temperature ( T m) have been located and from them, other related parameters of the glass have also been calculated. Visible absorption spectra of 45B 2O 3–5ZnO–(50 − x)PbO– xCuO ( x = 0. 1, 0.2, 0.5 and 1.0 mol%) have revealed two absorption bands at around 400 nm ( 2B 1g → 2E g) and 780 nm ( 2B 1g → 2B 2g) of Cu 2+ ions, respectively. Emission bands at 422 and 512 nm are found for the 1 mol% CuO doped glass with excitations at 306 and 332 nm.

Study of the structure and refractive parameters of diethylamine and triethylamine

The refractive index ( n ) and thermal coefficient of the refractive index ( d n / d t ) are measured at four wavelengths for the diethylamine and triethylamine. The measurements are carried out using the Bellingham+Stanley model 60/ED high-accuracy Abbe refractometer. The optical permittivity ( ε ) and its variation with temperature are calculated. Applying the Cauchy equation, the following refractive properties are obtained: the optical dispersion d n / d λ , the dielectric dispersion d ε / d λ , the variation of - d n / d T , d ε / d T , as a function of wavelength ( λ ), and Cauchy's constants against temperature. Additionally, molar refractivity versus temperature and wavelength are determined.

Determination of radial structural properties and spectral dispersion curves of poly(aryl ether ether ketone) fibre

AbstractPoly(aryl ether ether ketone) (PEEK) fibre was studied using a variable wavelength interferometric technique (VAWI). This technique was used in conjunction with a Pluta polarizing interference microscope to determine the spectral dispersion curves of fibre refractive indices and birefringence fibre. The results were used to calculate the dispersion properties of the fibre, ie dispersion and oscillation energies, Cauchy's constants of dispersion relation and the natural wavelength of the fibre. The radial refractive index and birefringence profiles were also determined, taking into consideration the refraction of light beam by the fibre, and some radial structural profiles were then calculated using a ring‐zonal model. The measurements of these radial profiles are required for optimizing the spinning and processing of manufactured textile fibres. The Fraunhofer diffraction pattern of a He–Ne laser beam was used to determine the average thickness of the fibre. Microinterferograms are presented for illustration. Copyright © 2003 Society of Chemical Industry

Determination of optical properties, dispersion, and structural parameters of poly(ethylene terephthalate) fibers using automatic variable wavelength interferometry technique

Automatic variable wavelength interferometry (VAWI) is used in combination with a Pluta double refracting polarizing interference microscope for measuring the spectral dispersion parameters of the refractive indices of poly(ethylene terephthalate) (PET) highly oriented yarn fibers (1000 denier/250 filaments). The resulting data are utilized to calculate the spectral dispersion and structural parameters such as Cauchy's constants, the dispersion energy, the oscillation energy, the density, the mean polarizability of the monomer unit, the number of monomer units per unit volume, the dielectric constant, the electric susceptibility, the optical orientation function, and the electric polarizability constant. Microinterferograms are given for illustration. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 1737–1742, 2003

The necessary requirements imposed on polar dielectric laser dye solvents—II

This paper is devoted to the experimental measurements of the refractive properties for five frequently used laser dye solvents: chlorobenzene, dimethyl formamide (DMFM), dimethyl sulfoxide (DMSO), glycerin and isobutanol. The refractive indices are accurately determined using the laser Mach–Zehnder interferometric technique. The variation of the refractive index n, its thermo-optic coefficients d n/d T, and the optical dispersion d n/d λ as a function of wavelength are calculated and represented. Moreover from the data, the temperature dependence of Cauchy's constants has been determined and a comparison between the studied solvents is made.

The necessary requirements imposed on polar dielectric laser dye solvents

A laser Mach–Zehnder interferometeric technique is applied to measure the refractive index n and its thermo-optic coefficient d n/d T for five important pure polar dielectric laser dye solvents (water, methanol, ethyleneglycol, butanol and acetic acid). The measurements are carried out using the argon-ion laser wavelength 514.5 nm, and He–Ne laser of λ=632.8 nm. Applying the empirical relationship of Cauchy between the refractive index and wavelength, the following properties are calculated and represented: The refractive index, the thermo-optic constant −d n/d T, the optical dispersion −d n/d λ as a function of wavelength and Cauchy's constants against temperature. On the other hand, a discussion for comparison between the investigated solvents are given.

Optothermal properties of fibers: 12-Interferometric investigation for thermally treated viscose fibers

The present article studies the structure of annealed viscose fibers interferometrically at a constant temperature of 100 ± 1°C at different times. The Pluta polarizing interference microscope has been used for determining the mean refractive indices and mean birefringence. The results were used to calculate the optical orientation function and the angle of orientation. The value (Δα/3α0), which depends on the molecular structure of the polymer, remains constant. Relationships between the mean refractive indices, birefringence, isotopic refgractive index, and polarizabilities per unit volume with different times were given for these fibers. The samples were subjected to X-ray diffraction to clarify the variation of crystallinity with the annealing conditions. Differential thermal analysis measurements were used to determine the glass transition temperature of viscose fiber. Measurements of the volume swelling parameter of the viscose fibers with different liquids were given. Also, determinations of Cauchy's constants, dispersive power, and dielectric constant at infinity were carried out. Illustrations are given using graphs and microinterferograms. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 361–369, 1999