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In sugar analysis two types of refractometers are generally used, the Abbe and the immersion. In both of these the method of grazing incidence is employed. If light passes from a rarer to a denser medium, the angle of refraction will be smaller than the angle of incidence. The largest angle of incidence is 90°, and therefore there will be a maximum angle of refraction (less than 90°). This angle is called the critical angle. Equation 59 then becomes

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In the Abbe refractometer, instead of actually reading the value of the critical angle in degrees and minutes and computing the index by means of a formula, the sector scale of the instrument is graduated directly in refractive indices, the intervals of which have been computed for the constants of the glass of the Abbe prisms. In making a determination with the instrument, the high-index prism is rotated about an axis perpendicular to the axis of the observing telescope until the border line of total reflection coincides with the intersection of the cross hairs of the telescope. Attached to the prism is an alidade with index, which moves along the graduated sector scale as the prism is rotated, permitting the reading of the index.

In the immersion refractometer the objective lens of the telescope. forms an image of the border line between the light and dark portions of the field on a scale engraved on the plane side of the collecting lens in the eyepiece.

In both the Abbe and the immersion refractometer, compensators are provided to permit the use of white-light illumination. In the Abbe instrument two Amici prisms, which rotate in opposite directions, compensate for the combined dispersion of the sample and prism and produce a sharp image of the dividing line. These compensating prisms furnish a means of measuring the dispersion.

(a) DISPERSION

The dispersion of a substance, (np-1/np-nc) may be calculated from the amount of rotation of the compensator prisms with respect to one another. np, ng, and no are the indices of the substance for the sodium line, the blue hydrogen line, and the red hydrogen line, respectively. By means of a drum on which is engraved an arbitrary scale, one of the Amici compensating prisms is rotated until the border line is achromatized and the scale reading taken. Suitable charts or tables are furnished by the manufacturers to facilitate conversion of the scale readings to values for the dispersion.

(b) EFFECT OF TEMPERATURE

Both the refractive index and the dispersion vary with change of temperature. For liquids the temperature coefficients generally are larger and negative. It is therefore essential that the temperature be known and be kept constant during observation. Most Abbe refractometers are provided with water-jacketed prisms, which permit the circulation of water at a constant temperature. These instruments are also fitted with suitable thermometers for indicating the temperature of the material and the prisms.

(c) ILLUMINATION

The refractometer may be illuminated by daylight. It has been found more satisfactory, however, to use an incandescent electric lamp of suitable intensity, provided with a shield to eliminate the disturbing influence of extraneous light.

(d) ADJUSTMENT OF THE INSTRUMENT

In many laboratories, the scale of the Abbe refractometer is frequently checked for adjustment, a practice which should be generally

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followed. Most instruments are furnished with a test plate made of special glass and whose index has been carefully measured and the value engraved on it. The test plate is applied to the upper prism with the polished end toward the light source, by means of a drop of monobromnapthalene. A series of careful readings is then taken, and the average value thus obtained is compared with the value engraved on the test plate. If necessary, the correction may be made by turning a small screw in the telescope tube, which moves the objective, causing the dividing line to shift.

(e) METHOD OF DETERMINING REFRACTIVE INDEX

Place a few drops of the solution on the polished face of the fixed prism and slowly bring the two prisms together and clamp them. To insure a sharp, clear image use sufficient liquid to fill the space between the prisms. Swing the instrument to an upright position and adjust the illuminating mirror so that the light source is reflected into the lower prism of the instrument. Rotate the compensating prisms to obtain a sharp colorless dividing line. Circulate water at a constant temperature, preferably 20° C, through the jackets of the prisms long enough to allow the temperature of the prisms and of the sample to reach an equilibrium, continuing the circulation during observations and taking care that constant temperature is maintained. If the determination is made at a temperature other than 20° C, correct the reading to the standard temperature of 20° C by means of tables 123 or 127, pp. 657, 664.

Caution must be observed if the humidity causes condensation of moisture on the exposed faces of the prisms. If such a condition exists, make the measurements at room temperature and correct the readings to 20° C by means of table 123 or 126.

Dark-colored solutions, such as molasses, are frequently difficult or even impossible to read on the refractometer. In such cases it is necessary to follow the procedure of Tischtschenko [9], who diluted the dark-colored solution with a pure sucrose solution of about the same concentration. Water should never be used, since such dilution introduces errors due to contraction in volume. The method employed is as follows:

Mix thoroughly a weighed quantity of the solution under examination (A) and a weighed quantity of a solution of pure sucrose of about the same concentration (B) whose sugar content has been previously determined by the refractometer. Obtain the refractive index of this mixture and, by means of table 122, p. 652, convert to percentage of dry substance. The percentage of dry substance in the sample in question is calculated by the formula:

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X=percentage of dry substance to be found,

A weight in grams of the sample mixed with B,

B=weight in grams of pure sucrose solution used in the dilution,

C=percentage of dry substance in the mixture A+B obtained from the refractive index.

D=Percentage of dry substance in the pure sucrose solution obtained from its refractive index.

In using the refractometer for determining the percentage of dry substance in solution, it is well to consider the effect of impurities, such as salts and organic nonsugars. Tolman and Smith [3] and others have shown that the instrument is applicable for determining the soluble carbohydrates in solution. The various sugars have approximately the same refractive index for equal concentrations. Stanek [10] has shown the effect of organic salts of sodium and potassium on the refractometric estimation of dissolved solids.

3. IMMERSION REFRACTOMETER

This instrument is designed for the measurement of solutions in bulk, but, with accessory prisms, may be used where only small quantities of solution are available.

Originally the immersion instrument of Zeiss [11] was designed with a single prism having a range of refractive indices from 1.32 to 1.36. The present design permits the use of interchangeable prisms, usually six in number, extending the range to 1.54. The arbitrary scale of the instrument, graduated in equal divisions from 5 to +105, is engraved on the plane side of the collecting lens of the

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eyepiece. The image of the border line is coincident with the scale. By means of the micrometer drum, readings may be made to tenths of a scale division. Each instrument is furnished with tables for converting the readings on the arbitrary scale to refractive indices. Since the relation between the arbitrary scales and refractive indices is not the same for all immersion refractometers, it is necessary to make the conversons by means of the tables furnished with the individual instrument.

The refractive indices corresponding to the scale divisions of the original single prism Zeiss immersion refractometer are given in table 32.

TABLE 32.-Refractive indices corresponding to the scale divisions of the original Zeiss immersion refractometer

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In the Bausch & Lomb immersion refractometer the six interchangeable prisms were furnished and have the following index ranges:

A, 1.32539 to 1.36639.

B, 1.36428 to 1.40608.
C, 1.39860 to 1.43830.
D, 1.43620 to 1.47562.
E, 1.47320 to 1.51335.

F, 1.50969 to 1.54409.

The adjustment of the scale of the instrument is made for each prism by means of a test solution or test plate.

With prism A the adjustment is made with distilled water; B, with a standard sodium chloride solution; C, with a test piece of fluorite; and D, E, and F, with glass test pieces.

The observations regarding illumination and temperature control of the Abbe refractometer also apply to the immersion instrument. The use of the immersion refractometer has been found advantageous by Bachler, [12], who devised a "one-solution method of analysis of sugar products," in which a sufficient quantity of a normal weight solution of the product is prepared and all or part of the necessary analytical data are obtained on this one solution. Certain changes were necessary in the immersion refractometer. At the suggestion of Bachler, the firm of Carl Zeiss, of Jena, produced an immersion refractometer with a single prism having a range of from no 1.331 to 1.372 and adjusted with distilled water at scale division 0. With the use of this instrument and the Goldbach flow-through cell, the method has been shown to give satisfactory results for factory control work.

4. SPECIAL REFRACTOMETERS

For special purposes there are available other types of refractometers. A pocket-type instrument is used for the estimation of the sugar present in the juice of the cane. Another special type is the factory refractometer, which is mounted on the vacuum pan and permits readings to be taken during the boiling process.

A new type of laboratory instrument is now in the course of manufacture by the Bausch & Lomb Optical Co. It is mounted in a horizontal position and illuminated by a sodium lamp. It combines features of both the Abbe and the immersion instruments and is capable of readings to a few units in the fifth decimal place.

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