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Abbe's Refractometer
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Aim 

 

  1. To find refractive index of the given liquid samples.
  2. To study the variation of refractive index with
  3. (a) temperature of the liquid sample.
    (b) wavelength of  the light source.
  4. To determine the polarisability of the given liquid samples at a given temperature.


Apparatus 

 

Abbe’s refractometer, temperature controller, light source and samples.


 

Abbe’s Refractometer

 

 The Abbe instrument is the most convenient and widely used refractometer, Fig(1) shows a schematic diagram of its optical system. The sample is contained as a thin layer (~0.1mm) between two prisms. The upper prism is firmly mounted on a bearing that allows its rotation by means of the side arm shown in dotted lines. The lower prism is hinged to the upper to permit separation for cleaning and for introduction of the sample. The lower prism face is rough-ground: when light is reflected into the prism, this surface effectively becomes the source for an infinite number of rays that pass through the sample at all angels. The radiation is refracted at the interface of the sample and the smooth-ground face of the upper prism. After this it passes into the fixed telescope. Two Amici prisms that can be rotated with respect to another serve to collect the divergent critical angle rays of different colors into a single white beam, that corresponds in path to that of the sodium D ray. The eyepiece of the telescope is provided with crosshairs: in making a measurement, the prism angle is changed until the light-dark interface just coincides with the crosshairs. The position of the prism is then established from the fixed scale (which is normally graduates in units of nD). Thermosetting is accomplished by circulation of water through the jackets surrounding the prism.


The Abbe refractometer is very popular and owes its popularity to its convenience, its wide range (nD = 1.3 to 1.7), and to the minimal sample is needed. The accuracy of the instrument is about ±0.0002; its precision is half this figure. The most serious error in the Abbe instrument is caused by the fact that the nearly glazing rays are cut off by the arrangement of to prisms; the boundary is thus less sharp than is desirable.

A precision Abbe refractometer, that diminishes the uncertainties of the ordinary instrument by a factor of about three, is also available; the improvement in accuracy is obtained by replacing the compensator with a monochromatic source and by using larger and more precise prism mounts. The former provides a much sharper critical boundary, and the latter allows a more accurate determination of the prism position.
 

Theory

 

 Measurement of refractive index


The refractive index of a substance is ordinarily determined by measuring the change in direction of colliminated radiation as it passes from one medium to another.

               (1)

Where v1 is the velocity of propagation in the less dense medium M1 and v2 is the velocity in medium M2; n1 and n2 are the corresponding refractive indices and θ1 and θ2 are the angles of incidence and refraction, respectively Fig 2.

When M1 is a vacuum, n1 is unity because v1 becomes equal to c in equation (1). Thus,

        (2)



Where nvac is the absolute refractive index of M2. Thus nvac can be obtained by measuring the two angles θ1 and θ2.

 

    Factors affecting refractive index


Various factors that affect refractive index measurement are


1. Temperature
Temperature influences the refractive index of a medium primarily because of the accompanying change in density. For many liquids, the temperature coefficient lies in the range of -4 to -6 x10-4deg-1. Water is an important exception, with a coefficient of about -1 x10-4deg-1.


2. Wavelength of light used.
The refractive index of a transparent medium gradually decreases with increasing wavelength; this effect is referred to as normal dispersion. In the vicinity of absorption bands, rapid changes in refractive index occur; here the dispersion is anomalous.


3. Pressure
The refractive index of a substance increases with pressure because of the accompanying rise in density. The effect is most pronounced in gases, where the change in n amounts to about 3x10-4 per atmosphere; the figure is less by a factor of 10 for liquids, and it is yet smaller for solids.
 

    Instrument for measuring refractive index


Refractometers: These based upon measurement of the critical angle or upon the determination of displacement of an image.


Critical angle Refractometers


The most widely used instruments for the measurements of refractive index are of the critical angle type. The critical angle is the angle of refraction in a medium when the angle of the incident radiation is 90° (the grazing angle); that is, when θ1 in above equation (1) is 90°, θ2 becomes critical angle θC. Thus,

         (3)

The fig: 3(a) illustrates the critical angle that is formed when the critical ray approaches the surface of the medium M2 at 90° to the normal and is then refracted at some point ‘o’ on the surface. Note that if the medium could be viewed at the end-on, as in fig.3 (b), the critical ray would appear as the boundary between a dark and a light field. However, the illustration is unrealistic in that the rays are shown as entering the medium at but one point ‘o’; in fact, they would be expected to enter at all points along with the same angle θC. A condensing or focusing lens is needed to produce a single dark-light boundary such as shown in fig: 3(b).

Fig: 3(a) illustration of the critical angle θC and critical ray and Fig: (b) end-on view showing sharp boundary between the dark and light fields formed at the critical angle. The critical angle depends upon wavelength. Thus, if polychromatic radiation is used, no single sharp boundary such as that in fig: 3(b) is observed. Instead, a diffuse chromatic region between the light and dark areas develops; the precise establishment of the critical angle is thus impossible. This difficulty is overcome in refractometers by the use of monochromatic radiation. As a convenient alternative, many critical angle refractometers are equipped with a compensator that allows the use of radiation from a tungsten source, but compensates for the resulting dispersion in such a manner as to give a refractive index in terms of the sodium D line. The compensator is made of Amici prisms, as shown in Fig: 4. The properties of this complex prism are such that the dispersed radiation is converged to give a beam of light that travels in the path of yellow sodium D line.
 

Fig: 4. Amici prism for compensation of dispersion by sample. Note that yellow radiation (sodium D line) suffers no net deviation from passage through the prism.

 

Polarisability


Using Claussius Mosotti relation, we can calculate polarisabilty of the given liquid. In S.I units

                   (4)

Where Є0 is electrical permittivity in free space, NA is Avogadro number; and for given the liquid sample ,αp is the polarisability , n is the refractive index, ρ is density of given liquid and M is molecular weight.

 

Temperature dependence of refractive index

 

The refractive index of a liquid varies with density, primarily because the density of liquids varies with temperature. One can approximate the dependence with the equation

            (5)

Where T0 is some standard temperature where the index of refraction n(T0) is the known index of refraction n at T0 , and  αT is the temperature coefficient of the index of refraction of the given liquid. Values of  αT vary, but they tend to be –0.0003 to –0.0004 for liquids with n < 1.63 (all of the liquids in this lab) and approximately –0.0007 for liquids with n > 1.63. For simplicity, we take  αT to be –0.0004.
 

Wavelength dependence of refractive index

 

The refractive index of a material varies with wavelength, a phenomenon which is called chromatic dispersion. In the visible spectrum, it can be represented to a good approximation by Cauchy’s equation

           (6)

Where A and B are constants that depend on the material, and is λ the vacuum wavelength. For example, at 20° C, for water A = 1.324 and B = 0.00319 μm2; and for ethanol, A = 1.352 and B = 0.00318.

 

 

 

 

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