Examples of interferometers. Examples of interferometers Determining the concentration of solutions using a Rayleigh interferometer

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STATE EDUCATIONAL INSTITUTION OF HIGHER PROFESSIONAL EDUCATION

DON STATE TECHNICAL UNIVERSITY

Department of Physics

Determining the concentration of solutions using a Rayleigh interferometer

Guidelines for laboratory work № 12

in physics

(Section “Optics”)

Rostov-on-Don 2011

Compiled by: Doctor of Technical Sciences, Prof. S.I. Egorova,

Ph.D., Associate Professor I.N. Egorov,

Ph.D., Associate Professor G.F. Lemeshko.

“Determination of the concentration of solutions using a Rayleigh interferometer”: Method. instructions. - Rostov n/a: Publishing center of DSTU, 2011. - 8 p.

Published by decision of the methodological commission of the faculty “Nanotechnologies and Composite Materials”

Scientific editor Prof., Doctor of Technical Sciences V.S. Kunakov

Goal of the work: 1. Study the principle of operation of the Rayleigh interferometer.

2. Study the phenomena of interference using a Rayleigh interferometer.

3. Determine the concentration of ethyl alcohol in water.

Equipment: Rayleigh interferometer, cuvettes with test solutions.

Brief theory

Interference - this is the superposition of coherent waves, in which a spatial redistribution of the light flux occurs, as a result of which maxima appear in some places and minima in light intensity in others.

Coherent waves of the same frequency and constant phase difference are called. To obtain coherent waves, it is necessary to split a light beam emanating from one source.

The interference pattern can be obtained using the ITR-1 device, which is based on the Rayleigh interferometer circuit, in which the interference pattern is obtained from two coherent light beams passing through two parallel slits (Fig. 1).

Light from source 1 (incandescent light bulb) is collected using a condenser on the slit 2 , located in the focal plane of the collimator lens 3 . A parallel beam of rays emerging from the lens is separated by two diaphragm slits 4 . These slits can be considered as two sources of secondary light waves that are coherent.

Coherent light beams pass through the lens 6 , and the upper part of the beams passes through the cuvettes 5 (Fig. 1), and the lower one is directly directed into the lens. As a result, interference of two pairs of coherent beams occurs in the focal plane of the lens. The interference pattern formed from two slits is a system of dark and light stripes. The position of the dark (minimum condition) or light (maximum condition) band is determined by the optical difference in the path of the interfering rays:

- maximum condition, (1)

- minimum condition, (2)

Where - optical path difference, which is equal to the difference in optical path lengths, i.e.
, (3)

Here
- refractive indices,
- paths traversed by light, - wavelength of light,
- order of maximum or minimum.

Observation is carried out through the eyepiece 7 (Fig. 1).

The interference pattern is shown in Fig. 2. Rays passing by the cuvettes form the lower interference pattern, and rays passing through the cuvettes form the upper one. The additional difference in the path of the rays in the cuvettes causes a displacement of the upper system relative to the lower one. If the cuvettes are filled with gases or liquids with different refractive indices, an additional path difference will appear, determined by formula (3).

Using a compensation device, the strip systems can be combined (Fig. 3).

In this work, the cuvettes are of the same length ( ). One of them contains distilled water, and the other contains a solution of ethyl alcohol in water. Therefore, the additional difference in the path of the rays is:

, (4)

Where - cuvette length,
are the refractive indices of the solution and distilled water, respectively.

Rayleigh interferometer

RAYLEIGH INTERFEROMETER (interference refractometer) - an interferometer for measuring refractive indices, based on the phenomenon of light diffraction on two parallel slits. The Rayleigh Interferometer diagram is presented in (Fig. 10) in vertical and horizontal projections.

A brightly illuminated slit of small width S serves as a light source located in the focal plane of the lens O 1 . A parallel beam of rays emerging from O 1 passes through a diaphragm D with two parallel slits and tubes R 1 and R 2 into which the gases or liquids under study are introduced. The tubes have the same lengths and occupy only the upper half of the space between O 1 and the telescope lens O 2. As a result of the interference of light diffracting on the slits of the diaphragm D, in the focal plane of the lens O 2, instead of the image of the slit S, two systems of interference fringes are formed, schematically shown in Fig. 10. The upper system of stripes is formed by rays passing through the tubes R 1 and R 2, and the lower one by rays passing past them. Interference fringes are observed using a short-focus cylindrical eyepiece O 3 . Depending on the difference in the refractive indices n 1 and n 2 of the substances placed in R 1 and R 2, the upper system of bands will be shifted in one direction or another. By measuring the magnitude of this mixing, n 1 - n 2 can be calculated. The lower system of strips is stationary, and the movements of the upper system are measured from it. When the slit S is illuminated with white light, the central stripes of both interference patterns are achromatic, and the stripes located to the right and left of them are colored. This makes it easier to detect the center stripes. Measuring the movement of the upper system of strips is carried out using a compensator, which introduces an additional phase difference between the rays passing through R 1 and R 2 until the upper and lower systems of strips are combined. Using a Rayleigh interferometer, very high measurement accuracy is achieved up to the 7th and even the 8th decimal place. The Rayleigh interferometer is used to detect small impurities in air, water, for the analysis of mine and furnace gases and for other purposes.

Fabry-Pérot interferometer

FABRY-PEROT INTERFEROMETER is a multi-beam interference spectral device with two-dimensional dispersion, with high resolution. Used as a device with spatial decomposition of radiation into spectrum and photogr. registration and as a scanning device with photoelectric registration. The Fabry-Perot interferometer is a plane-parallel layer of optically homogeneous transparent material, limited by reflective planes. The most widely used air Fabry-Perot interferometer consists of two glass or quartz plates located at a certain distance d from each other (Fig. 11.). Highly reflective coatings are applied to the planes facing each other (made with an accuracy of 0.01 wavelengths). the Fabry-Perot interferometer is located between the collimators; An illuminated diaphragm is installed in the focal plane of the input collimator, serving as a light source for the Fabry-Perot interferometer. A plane wave incident on a Fabry-Perot interferometer as a result of multiple reflections from mirrors and partial output after each reflection is broken into a large number of plane coherent waves that differ in amplitude and phase. The amplitude of coherent wills decreases according to the law of geometric progression, and the difference in the path between each adjacent pair of coherent wills moving in a given direction is constant and equal

where n is the refractive index of the medium between the mirrors (for air n=1), and is the angle between the beam and the normal to the mirrors. Having passed through the lens of the output collimator, coherent waves interfere in its focal plane F and form a spatial interference pattern in the form of rings of equal inclination (Fig. 12.). The intensity (illumination) distribution in the interference pattern is described by the expression

I =f k BTу/f 2 2,

where B is the brightness of the source, f k is the transmittance of the collimator lenses. y is the cross-sectional area of the axial parallel beam, f 2 is the focal length of the output collimator lens, T is the transmission function of the Fabry-Perot interferometer.

T= T max (1+з 2 sin 2 k?) -1

Where T max = , k = 2r/l

z = 2/(1- c), f, c and a are the transmittance, reflection and absorption coefficients of the mirrors, respectively, and f + c + a = 1.

The transmission function T, and therefore the intensity distribution, has an oscillating character with sharp intensity maxima (Fig. 13), the position of which is determined from the condition

where m (integer) is the order of the spectrum, l is the wavelength. In the middle between adjacent maxima, the function T has minima

Since the position of the interference maxima depends on the angle u and the angle h equal to it of the exit of the rays from the second glass plate, the interference pattern has the form of concentric rings (Fig. 12), determined from the condition localized in the region of the geometric image of the input diagram (Fig. 11) .

The radius of these rings is equal, which means that at m = const there is an unambiguous relationship between r m and r and, therefore, the Fabry-Perot interferometer produces a spatial decomposition of the radiation into a spectrum. The linear distance between the maxima of neighboring rings and the width of these rings (Fig. 13.) decrease with increasing radius, i.e., with increasing r t, the interference rings become narrower and denser. The width of the rings?r also depends on the reflection coefficient c and decreases with increasing c.

The aperture ratio of a real Fabry-Perot Interferometer is several hundred times greater than the aperture ratio of a diffraction spectrometer with equal resolution, which is its advantage. Since the Fabry-Perot interferometer, having a high resolving power, has a very small dispersion region, when working with it, preliminary monochromatization is necessary so that the width of the spectrum under study is smaller. For this purpose, crossed dispersion instruments are often used, combining a Fabry-Perot interferometer with a prism or diffraction spectrograph so that the directions of the dispersions of the Fabry-Perot Interferometer and the spectrograph are mutually perpendicular. Sometimes, to increase the dispersion area, a system of two Fabry-Perot Interferometers placed one behind the other with different distances d is used, so that their ratio d 1 / d 2 is equal to an integer. Then the dispersion region is determined by the “thinner” Fabry-Perot Interferometer, and the resolving power is determined by the “thicker” one. When installing two identical Fabry-Perot Interferometers, the resolving power increases and the contrast of the interference pattern increases.

Fabry-Perot interferometers are widely used in the ultraviolet, visible and infrared regions of the spectrum to study the fine and ultrafine structure of spectral lines, to study the mode structure of laser radiation, etc. The Fabry-Perot interferometer is also used as a resonator in lasers.

Rayleigh interferometer

Rayleigh interferometer circuit

Rayleigh interferometer- single-pass double-beam interferometer, dividing the light from the source into two streams, phase difference between which is created by passing light through two identical cuvettes, filled with different gases. First proposed Lord Rayleigh in 1886. Used to determine refractive index gases

Schematic diagram

Light from the source is passed through lens, creating a parallel beam and apertures, cutting out two beams from it (interferometer arms). Each beam passes through its own cell with gas. At the output of the circuit there is a lens that brings both beams together to produce interference fringes in its focus.

For measurements, a compensator is inserted into one of the arms - for example, a glass plate, by turning which you can change optical path length beam in the shoulder. If the refractive index in one of the arms is equal to n, then the second unknown refractive index is equal to

where is the length of the cuvette with gas, - wavelength light source, - interference order (the number of interference fringes intersecting at a given point). With typical setup parameters - a cell length of one meter, a wavelength of 550 nm and an interference order of 1/40 - a refractive index difference of 10 −8 can be measured. The sensitivity of the interferometer is determined by the length of the cell. Its maximum length is usually determined by the technical capabilities of temperature control, since thermal fluctuations will distort the refractive indices of gases.

Literature

Max Born, Wolf, Emil ( English Emil Wolf) Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. - 7th. - CUP Archive, 2000. - P. 299-302. - 986 p. - ISBN 9780521784498
P. Hariharan Basics of interferometry. - Academic Press, 2007. - P. 15. - 226 p. - ISBN 9780123735898

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