Determination of the concentration of solutions using a Rayleigh interferometer. Interferometers and their applications Rayleigh interferometer

Rayleigh interferometer

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Description

The Rayleigh interferometer is one of the most sensitive interference devices to the difference in phase incursions of waves, which allows it to be used to accurately determine the refractive indices of gases at a pressure close to atmospheric (at this pressure, the corresponding refractive index differs from unity in the fourth to fifth decimal place) .

A schematic representation of the design of the Rayleigh interferometer is shown in fig. one.

Schematic representation of the design of the Rayleigh interferometer

Rice. one

A beam of light from an almost point source S, which is at the focus of the lens, is converted by this lens into a parallel beam. Further, behind the lens, there is a diaphragm with two holes symmetrical about the main axis of the system - secondary sources S 1 and S 2, forming two parallel thin beams. These beams are then focused by a second lens onto a screen located in its focal plane. The result is an interference pattern of horizontal stripes, as shown in the figure. In this case, in the absence of additional objects with refractive indices n 1 (a cell with the gas under study) and n 2 (a phase shift compensator with a known controlled phase shift of the optical radiation in it), the zero maximum of the interference pattern lies on the system axis. The zero maximum is the maximum corresponding to the zero path difference D of the waves forming the interference pattern. When using broadband radiation (for example, natural light), it is easily distinguished from the higher-order maxima m:

D \u003d m l 0,

where l 0 is the central wavelength of the radiation spectrum.

Indeed, it is easy to understand that it is the only one that has the initial white color, while the higher-order maxima are “stretched into the spectrum” due to the fact that the maximum conditions are achieved at different displacements from the center of the pattern for different wavelengths of the beam spectrum.

If we now introduce into two beams propagating in the interlens space (the so-called interferometer arms) a cell of length L with the gas under study n 1 and a controlled optical delay n 2 (for example, the same cell with a gas whose refractive index depends on pressure is known) , then the beams will receive an additional path difference:

D 1 \u003d L (n 2 -n 1 ).

Thus, the zero fringe of the interference pattern will shift, and the center of the field will acquire color.

To “return the picture to its place”, it is necessary to equalize the refractive indices of the studied gas and the reference gas in two cuvettes, which is achieved by varying the pressure of the latter. As a result, having restored the centrality of the zero “white” band (and this can be done with high accuracy, on the order of 1/40 of the band, D m Ј 1/40 ), we obtain accurate information about the refractive index of the gas under study. Real instruments, made according to the scheme of the Rayleigh interferometer, make it possible to measure the differences in the refractive index from unity according to the formula:

(n-1)= l 0 D m/L » 10 -8 .

Timing

Initiation time (log to -8 to -7);

Lifetime (log tc -7 to 15);

Degradation time (log td -8 to -7);

Optimal development time (log tk -6 to -5).

Diagram:

Technical realizations of the effect

Schematic diagram of the Rayleigh interferometer

Rayleigh interferometer- a single-pass double-beam interferometer that separates light from a source into two streams, the phase difference between which is created by passing light through two identical cuvettes filled with different gases. It was first proposed by Lord Rayleigh in 1886. Used to determine the refractive indices of gases.

circuit diagram

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

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

n ′ = n + λ 0 ℓ Δ m , (\displaystyle n"=n+(\frac (\lambda _(0))(\ell ))\Delta m,)

where ℓ (\displaystyle \ell )- length of the cuvette with gas, λ 0 (\displaystyle \lambda _(0)) is the wavelength of the light source, ∆m (\displaystyle \Delta m)- the order of interference (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 cuvette. Its maximum length is usually determined by the technical possibilities of temperature control, since thermal

7. Rayleigh interferometer

Rayleigh pnterferometer (interference refractometer) - an interferometer for measuring refractive indices, based on the phenomenon of light diffraction on two parallel slits. The diagram of the Rayleigh Interferometer is shown 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 objective O 1 . A parallel beam of rays emerging from O 1 passes through a diaphragm D with two parallel slots and tubes R 1 and R 2 into which the studied gases or liquids are introduced. The tubes are of equal length and occupy only the upper half of the space between O 1 and the telescope objective O 2 . As a result of the interference of light diffracting on the aperture slits D, two systems of interference fringes are formed in the focal plane of the objective O 2 instead of the image of the slit S, which are schematically shown in Fig. 10. The upper system of bands is formed by rays passing through the tubes R 1 and R 2 , and the lower one by rays going past them. The interference fringes are observed using a short focus cylindrical O 3 eyepiece. 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, one can calculate n 1 - n 2 . The lower system of strips is motionless, and the displacements of the upper system are counted from it. When the slit S is illuminated with white light, the central fringes of both interference patterns are achromatic, and the fringes to the right and left of them are colored. This makes it easier to find the center bands. The measurement of the movement of the upper stripe system is carried out by using a compensator, which introduces an additional phase difference between the beams passing through R 1 and R 2 until the upper and lower stripe systems are aligned. With the Rayleigh interferometer, a 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, in water, to analyze firedamp and furnace gases, and for other purposes.

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