The Interference Microscope as Refractometer for Liquids

The interference microscope makes it possible to measure the optical path difference, and thereby the refractive index, of two laterally separated features. In this paper its application as a refractometer for liquids is described.

In order to obtain a permanent lateral separation between the liquid and the reference area, a special liquid holder was designed. This consists of two semicircular glass plates whose diametrical surfaces are optically worked and maintained in close mutual contact. A quadrant of one of the plates is optically worked to form a wedge having an angle of approximately 10 degrees (fig. 1). The semicircular elements are cemented with Araldite to a glass base plate having a hole of about 5 mm radius concentric with the compound disk formed by the diametrically-contacted elements. This design makes it possible to avoid spoiling the diametrical interface with surplus cement, because the cement is confined to the perimeter of the compound disk. A wedge of liquid is obtained by placing approximately 0.1 ml of the liquid under a cover-glass on the disk.

The one flat half of the glass disk will serve as the reference area and the cut edge as a sharp boundary. As the depth of the liquid is continuously increasing along the wedge, a system of evenly spaced fringes will be observed when the glass disk is viewed through the microscope in monochromatic light (fig. 2, A). The thickness of the glass disk necessitates an objective of sufficiently long working distance; the 10X objective is therefore used. The length of the fringes will be 330/x, which is the lateral dimension of the shearing area of this objective.

A fringe will appear whenever the optical path difference between the reference area and the liquid increases by one wavelength. If the layer thick-ness of the liquid at the place of the first fringe is t, the next fringe will appear at the place where the layer thickness is 2t, the next at 3i, &c. : so the difference in layer thickness between two consecutive fringes is t. The numerical value of t depends upon the difference between the refractive index of the glass n_g, and that of the liquid n_m. The greater this difference is, the smaller is the numerical value of t and a greater number of fringes per unit length is observed. When n_m decreases fewer fringes will appear and

Fig. 2, B depicts the appearance of the fringes for liquids of different refractive indices.

The measurement of the refractive index of a liquid is carried out either by measuring the distance between two consecutive fringes or, as we prefer, by counting the number of fringes per unit length, the fractional part of a fringe being measured by the use of the phase-measuring goniometer of the microscope. Fig. 3 shows the results of a series of measurements of liquids of different refractive indices. As seen from this figure—and from equation (1) —there is a linear relationship between the refractive index and the number of fringes per unit length.

from which, as N, K, and n_g are known, n_m can be calculated.

As the true value is always unknown, the accuracy of a measurement is a matter of probability. As the degree of accuracy obtainable with this refractometer obviously depends upon the accuracy with which the fractional part of fringes can be determined, the standard deviation from a series of determinations of fractional fringes will be used as a measure for this probability.

Fig. 2, B shows that the width of the fringes increases as the difference between n_g and n_m decreases, and it might therefore be thought that the precision with which fractional fringes could be determined would depend upon the fringe width. That this is not the case is evident from results of measurements of fractional fringes in water and liquid paraffin. From io determinations in water the mean was found to be 0’4161 fringe with a standard deviation (s) of 0-01561 fringe and for liquid paraffin the mean was 0-1506 fringe with a standard deviation of 0-01214. As the variances of the two sets do not differ significantly (F — 1 · 65; 0 · S7 < P < 0-9), it can be concluded that the fringe width has no effect upon the precision. Further, five sets of 10 determinations of fractional fringes for different liquids—at room temperatures ranging from 20° C to 25° C—showed, as judged by Bartlett’s test, identical variances. These were therefore combined, yielding a standard deviation of 0-01428 fringe. As the mean value of a normal distribution is being considered as the best estimate of the true value, this numerical value of the standard deviation means that in 99 out of 100 cases a single measurement will deviate o· oo1 or less in refractive index from the mean, or true value. This accuracy can be improved upon by repeating the measurement. If, for example, two determinations are carried out, either by repeating the measurement on the same unit length or by measuring on two unit lengths, the deviation from the mean would be 0· 0007 or less in refractive index.

The accuracy obtainable with this instrument compares favourably with the accuracy obtained by other micro-methods (Bauer, 1949; Jelley, 1949), where the accuracy varies between 0· 005 and 0· 0005 in refractive index.

The work of one of the authors (S. I.) is supported by a grant from the British Empire Cancer Campaign.