Microscopical Determination of Refractive Index with an Error of about &0.00001 Charles Proffer Saylor National Bureau of Standards, Washington,DC 20234
Steep optical-glass prisms in contact with the liquid being measured bend a collimated monochromatic beam. The deflected beam enters the microscope, and an image of the target forms at the back focal plane of the Objective. The distance of the Image from the center is proportional to the sine of the angle of deviation and rigorously related to determinable constants of the system and the refractive index of the liquid. Accuracy Increases with steepness of prism, but the refractive index range served by any one is thereby reciprocally decreased. Sine of the angle of deflection, angle of the particular prism being used, and the refractive index of the prism are sufficient for direct calculation of the refractive index of the liquid. When the angle of the prisms Is achieved. Each prism (with a is 72', an accuracy of numerical aperture of 0.11) can then serve a range of only 0.06 In Index. This necessitates a series of prisms of selected optical properties, each serving 0.05 In Index and providing a comfortable overlap. About 1 cubic millimeter of liquid is required for a full determination.
Among physical properties of transparent liquid chemical substances, only freezing point has potential analytical usefulness as great as refractive index. While refractive index does not, like freezing point, have the advantage of providing inherent evidence of purity, the ratio of the probable error of a single determination to the broad range within which most materials cluster is among the most favorable. No other property can be measured more simply or quickly with equivalent accuracy ( I ) . Within the range of their usefulness (ordinarily about 1.3 to 1.75) and for general purposes, the direct-reading critical-angle types of refractometer such as the Abbe or the dipping refractometers are usually preferred. For smaller samples, for materials on which the refractive index is below 1.3 or above 1.75, or for those which cannot be placed on the prism of an Abbe refractometer, a variety of microscopical methods have been developed. With all direct microscopical methods that are in use for liquids, the ultimate errors of the result equal or exceed 0.001. Microscopical measurements of solid fragments in liquid are much better. For example, using a phase microscope and hot stage, Ojena and DeForest ( 2 )have achieved an accuracy of f0.000034. I t is the intention in this paper to describe a method by which microscopical determinations of refractive index can, in principle, be performed with an arranged accuracy. Specifically, with the selected constants for the individual parts, the apparatus which is described permits measurements in which the errors of a single determination are about 0.00001.
USUAL MICROSCOPICAL METHODS OF DETERMINING REFRACTIVE INDEX OF LIQUIDS The method of the duc de Chaulnes ( 3 ) ,extensively used on crystalline materials, particularly by European observers, can also be used with liquids. I t depends on the famil1114
ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
iar phenomenon that makes the bottom of the filled bathtub appear to lie above its true position. The technique utilizes the approximation that the ratio of the true depth of a cell to its apparent depth equals the refractive index. One unresolved fault precludes the attainment of high accuracy. In order to achieve precise measurements of the vertical displacement of the image of a mark on the bottom of a cell, it is necessary to utilize a rather large angular aperture in the observing system, whereas the assumed equation for refractive index is strictly true only a t the limit where the aperture approaches zero. The publication by the duc de Chaulnes (3) is generally inaccessible, but good descriptions of his lucid account are given in the various editions of Johannsen's Manual of Petrographic Methods ( 4 ) . F. E. Wright ( 5 ) described a number of microscopical methods. The one which he considered best operates on the same general principle as the Abbe refractometer. An undercut inclined glass surface, in contact with the liquid being determined and illuminated in all directions by contact with an underlying ground glass prism of equal angle, yields a limiting ray a t the critical angle for the liquid-glass interface. With a Bertrand lens, the back focal plane of the objective is focused so that its image falls on the scale of a micrometer eyepiece. The position of the line between the dark and bright portions of the field is governed by the critical angle. The attainable accuracy is limited by the fact that the entire range of measurable refractive index occurs as one continuous span within the field of the eyepiece. The sensitivity changes from end to end of this range, involving both the angle in the glass and that of its emergence into the space above the coverglass. Related to another of the methods tried by Wright but rejected by him is that of Nichols. Nichols (6) utilized two opposed prisms which are placed above a line on a microscope slide. The apparent distance between the two images of the line as displaced by the prisms is employed to measure the refractive index. A doubling of accuracy occurs because of the opposite displacements of the two images. A further increase in accuracy occurs because vertical displacement between the two deviated images of the line beneath the prisms is avoided. The horizontal displacement of these images of the line takes place, of course, a t the surface between the prism and the liquid. I t depends for its magnitude upon the distance between the reference line and the position on the inclined surface through which the measuring rays pass. If the vertical distance were zero, there would be no displacement. The relation between the displacement and the refractive difference is thus difficult to calculate. [The article by Nichols (6) is hard to secure. A satisfactory description is given in Reference (7).] Each of the foregoing devices has depended on a calibration using known liquids. Accuracy is further limited by the facts that different parts of the aperture of the objective correspond to different displacements and that the entire refractive index range must be covered by the displacement of an image across the field of the micrdcope. T o cover the range from 1.3 to 1.8 with an accuracy of one in the fourth decimal place, assuming a displacement linear with refrac-
tive index, it would be necessary to measure the five-thousandth part of the field diameter. Although this might be possible by a careful control of conditions, it does not appear to have been attempted.
DIFFERENTIAL REFRACTOMETER PRINCIPLE AS APPLIED TO THE MICROSCOPE It seemed reasonable to attempt to determine the refractive index of a liquid microscopically by measuring the change of direction of a collimated beam as it passes from the inclined surface of a reference material into the substance of question. Such, for large samples, was the principle of the Zeiss Differential Refractometer, a commercial instrument which this worker has never found described in the permanent literature. That instrument was made in the early part of this century and was presumably intended for the estimation of sugar concentrations. An inclined glass plate separated the solution from its solvent which differed in index only slightly. The incident and refracted beams were spontaneously collimated. A small deviation was approximately proportional to a small difference in refractive index. A less elegant though more elaborate manifestation is the refractometer of Brice and associates (8). This instrument has the fault that the beam is only approximately parallel as it passes the liquid solution interface. Different parts of the viewing aperture indicate different refractive indices. As the aperture is changed by opening or closing the iris diaphragm, the apparent refractive index is raised or lowered, depending on whether the converging lens precedes or follows the divided cell. The differential refractometer of P. P. Debye (9) and certain contemporary commercial instruments avoid the errors originating from this inadequacy of collimation. With Jelley’s (10) refractometer, one sights a t a horizontal slit in a card through an inclined glass-liquid interface and sees the displaced image of the slit, illuminated by monochromatic light, against a scale calibrated in refractive index. The device is substantially free from the systematic error that characterizes the Brice et al. refractometer, but since it covers the range from 1.330 to 2.00 in one pattern, the accuracy (which is greatest a t low indexes) has a general uncertainty of about fO.OO1. The device to be described here is similar to the foregoing differential devices, of which the Zeiss instrument is the prototype. I t was briefly mentioned in another publication (11).It can achieve accuracy in the fifth decimal place over most of its range. In one sense, however, it differs from the differential refractometers since it does not compare two liquids of similar refringence separated by a septum. It utilizes, instead, a group of masters, a graduated series of parallel glass prisms of known index, each of which is intended to serve over a limited range. With any sample, determination of index is executed with the prism suited to the refractivity as observed. A centered reference marker is strictly at the lower focal plane of a well corrected condenser or a low powered objective used as a condenser. Alternatively, a very distant light source with slit or fiducial marker and no condenser may be used. Parallel monochrlomatic light passes through the object plane of the microscope. The light which has come through the position of the centered marker will be not merely parallel; it will also be parallel to the axis of the microscope. If, as in Figure 1,it passes into an optical glass of refractive index N having an upper plane surface inclined to the horizontal by the angle A and if the sample having the index of refraction n, lies between the inclined surface and a coverglass, the beam will experience two changes of direction and emerge from the coverglass inclined from the vertical by the angle o (passages through the slide and coverglass cause no net
t Figure 1. The cell A collimated beam is not deflected when it enters the prism of angle A . Deflection at the prism-liquid interface is p. On passing from the liquid to air, the final deviation becomes 0.Deflection (and therefore 0 ) may be either positive (away from the interface) or negative (toward the interface)
change of direction since top and bottom surfaces of both are parallel). The angular deviation is given by the relation: sin o = sin A d n 2 - N2 sin2 A
- N sin A cos A
(1)
This relation is similar in principle to the one used by Jelley (IO):differing chiefly in that light first enters the fixed prism. As a result, the equation is greatly simplified and can be arranged so that n occurs on the right only once. It is derived as follows: sin o = n sin p r=A-p n sin r = N sin A
.....................
.......................... N sin A = n sin ( A - p ) = n sin A cos p - n sin p cos A N s i n A = n s i n A 1-- sin2 p - sin o cos A N sin A = sin A d n sin2 o - sin o cos A sin A d n 2 - sin2 o = sin o cos A + N sin A n2 sin2 A - sin2 A sin2 o = sin2 o cos2 A + 2 N sin A cos
24 -0.032222 -0.~28942 -C.325683 -0.522445
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1.64C -3.007813 -0.0075C0 -0.037186 -3.006873 -C.l06560 -0.006248 -C.Ot5935 - -ti*---e.ae+fAxT*.6??-+375 :.3e4-%3L * > C ?*.? -C-;@?%3---l-30 -3.30282% 1.642 -0.001578 -C.001268 -0.000959 -J.000649 -0.3n0340 -0.900G31 C.CJS276 1.643 0.001512 0.001820 0.002128 0.902435 (1.302743 0.003350 G.C>3357 1.644 i1.004584 3.504890 0.305197 0.005502 6.Sn5808 0.0C6114 C.OC6419 1.645 -3.007639 0.007944 0.008248 3.0C8552 0.008U56 3.009160 ?.039464 1.646 0.010677 0.010980 0.011282 0.911585 C.011887 0.012189 C.012491 -0 - r P d.uiW---.e.E+%9€ft---6;-4fftef.- t*5,%t-2 1.648 0.016702 0.0170C2 0.017301 0.017600 e.017899 3.918198 ?.G18497 1.649 0.019690 0.019988 0.023286 ii.32C564 0.320881 0.021178 0.021475
1.650
7
0.032070 u.032361 0.034978 0.335268 0.037872 u.03b161 0.041039 3.345151 5.043903 0.343617 0 . 1 4 6 4 6 L IT 3 4 6 7 5 3 ,.349399 0.349336
0.023847 0.226797 -373290.932653 0.1) 3 5 5 5 8 0.938449 C.041326 C. 0 4 4 188
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6.C45614 0.C48456 5.251255
0.0396:9 3.0427>H
Figure 4. Illustrative portion of reference tables Refractive index of liquid and corresponding change in sine. Interpolation over index differences of 0.001 will introduce no error in the fifth place
stage is rotated 180' between readings. The focal length of the lower condenser element is about 30 mm. The upper element is not used. Parallel radiation therefore from any point in the reference system passes through all parts of normal object plane at B. At B is the refractometer cell. The light passes first through the lower, horizontal surface of a carefully ground and polished optical glass prism, then through the surface of contact with the liquid being measured, inclined at an angle of about 72' from horizontal where its direction is changed by refraction. It continues, still as a collimated parallel beam, to the plane parallel coverglass where after two refractions (which may be interpreted as one) it emerges and passes to the objective. The two deflections-at the prism-liquid contact and at the surface of the cell-are both zero when the indexes of refraction of liquid and prism are the same, but increase with increasing difference in refractivity, being deflected toward the medium of lower index of refraction. Leaving the cell B, Figure 3, which is 1.8 mm deep, the light travels 35 mm and passes into a 3.2X, 53-mm EF, 0.11-NA achromatic objective. The parallel bundle that bypasses the prism surface is focussed by the objective and forms an image 111 of the target a t the back focal plane of the objective exactly at its center. The parallel bundle that has emerged from the inclined surface also has its rays collected into an image 112 of the target which, however, will not in general be at the center. The distance between 111
and 112 is, so far as can be measured, exactly proportional to the sine of the total deflection a t the cell. To measure the distance between 111 and 112, the light passes up the tube of the microscope and into a 5 X Huyghenian eyepiece where, at the image plane, there is a small rectangular diaphragm, hinged so that it can fall into or be removed from the image plane. This diaphragm serves to isolate the light that has passed through the inclined surface of the prism and also that which has passed the flat bottom of an equal adjacent area. The entire microscope is focused at the level of this diaphragm before the hinged diaphragm, which has a piece of iron along one side, is caused to fall into place by the movement of a permanent magnet externally controlled. With the field limited to radiation which passes through the diaphragm, the monochromatic light passes out of the eyepiece D, Figure 3, and at the exit pupil, 111, 12 mm above its top surface, images of 111and 112 are formed. One of these corresponds to light that has been deflected at the prism-liquid interface and the other to undeflected light. Above the eyepiece, a cap-form, 25X filar micrometer eyepiece, E, Ramsden style is placed. Its fiducial mark can be adjusted vertically so as to be a t the same level as the images of 111 and 112. Its eye lens can be adjusted so that the observer will find both fiducial mark and the images of the target to be in a comfortable state of focus. T o determine the refractive index of the liquid, the disANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
1117
Figure 6. Field at image plane of the 5X eyepiece ( a )(Len). Three adjacent prisms are seen. The Center one has an index near that Of the liquid. the others about 0.05 different. ( b ) (Right). The magnet operated diaphragm has been dropped in place. The prism appears to the right and the fiat surfaceof the glass to the leR
Figure 5. The assembled cell The nearest prism is fused quartz. The other seven extend upward and to the left The indexes of the prisms. wrinan in drawing ink. can be read if the page is inverted
tance between 1111 and 1112, the images of 111 and 112, is measured. Then, from tahles or from calculations based upon previously measured constants, the index of the refraction of the liquid is evaluated. A representative portion from such a table is shown in Figure 4.
THE DEFLECTING CELL The assembled working cell is shown in Figure 5. Seven optical glass slahi, 1 millimeter wide and 1.8 mm high have slanting ends, inclined slightly more than 72' from horizontal. The bottom plate is formed from a Sedgewick-Rafter coverglass and the top plate from the thin form of polished haemocytometer coverglass. The slanting end surfaces of the slabs project in the microscope object field as 1-mm squares. Together with the liquid being measured, they are the prisms. Each serves as the heart of the refractometer for its own part, about 0.064, of the refractive index range from 1.495 to 1.819, thus providing about 0.018 of overlap between prisms. An eighth prism, shown in the foreground, is made of fused quartz. In order to extend its range, i t was made with an angle slightly less than 60'. The refractive index range with this extends down to 1.403 but with an uncertainty of about f0.00002. By substituting a microscope objective of numerical aperture 0.25, the range extends to 1.333 with another doubling of the uncertainty As shown in the figure. the eight prisms arc ilirnked by t w o wider dahs of nrism t _. w e elass hut Iuwer outical aualitv. . " Because of the method of making these prisms, the raw materials of about 10 cells were completed whereas only one was required. So far as possible, the other sets of prisms will be issued on request, to responsible persons or laboratories with need and the expectation of making effective use of them. The entire system is cemented together with ordinary corn syrup. This resists attack hy most liquids and can he cured in place in a low temperature oven until it becomes optically homogeneous. The assembly is best performed in two stages. The coverglass is laid on a hard flat surface and a thin strip of corn syrup drawn from end to end near the center of where the prisms and end pieces will stand. These are inserted in the proper locations, pressed in place, and a cushion and weight placed on top. By leaving the unit in an oven a t about 50' for several days, the layer of cement thins and hardens. Any excess cement can be washed off with water without damaging the thin contact layer. A similar routine can then be followed to join the slide to the hottom of the prisms. At this point, because of the stahility in I
1118
ANALYTICAL CHEMISTRY, VOL. 47, NO. 7. JUNE 1975
position of the prisms, the correct amount of cement can be added. An insignificant amount will extrude from between the plate and the prisms. Angles are stabilized by the thinness of the film between the prisms and the under surface of the coverglass; the angle between the coverglass and the prism face is the same as the measured angle on the prism. Whenever attack happens, such as can follow repeated measurement of the lower alcoho!s, there are no serious consequences. The device is soaked apart with water, and an appropriate replacement of cement is made. Figure 6a shows the image of a few of the prisms as they are seen in the eyepiece, D of Figure 3. When the diaphragm is dropped, Figure 66, the light which passes is limited to the projected inclined plane of one prism and an equivalent area where the flat top of the prism is cemented to the coverglass or where the flat bottom of the chamber is exposed. Fortunately for the construction of this apparatus, our laboratories had available a selection of optical glasses that had been made during or immediately before World War 11. L. W. Tilton had measured the refractive indexes by the minimum deviation method using 4-cm ground and polished 60' prisms and a precision goniometer. From these glasses, seven were chosen on the basis of the spread of refractive index. With one exception, the errors in refractive index measurement were small in the sixth decimal place although by a convention they are reported only to the fifth. The refractive indexes of the prisms are shown in Table I for 3 w a v e l ~ n y r h ~ . T i l t u n had rcr)urted the index of glass I only to the rhird . decimal place. This was because inhomogenieties had degraded the image of the target as seen through the 4-cm prism. The individual 1.8- X 1.0-mm mini-prisms turned out to be fully satisfactory, however. The refractive index on any one prism can he effectively determined by a reversal of the ordinary process. Thus, by choosing a liquid that lies in the range of both this and a n adjacent prism and measuring the displacement against the known prism, n f o r the liquid can he determined and from that N for the prism. As an example, a mixture of 9 parts methylene iodide and 1 part 1,2-dichlorohenzene (IO) has an index of about 1.72. I t lies easily within the range of both number 6 and number 7 prisms. Although the vapor pressures of both constituents are fairly high, the partial pressures are so nearly proportional to composition that the liquids do not detectably fractionate during a period many times longer than is required for the comparison. The values on prism 1are taken from recorded values for optical fused crystalline quartz. Values found by Malitson (13) for fused silica glass made from chemically prepared
oxide differ somewhat. At the same wavelengths, he found 1.45637,1.45840,and 1.46313.
THE MATTER OF ATTAINED ACCURACY The completed device is free from dependence upon calibration with comparison samples. I t is, instead, a direct instrument except to the extent that the refractive index of the component glasses has been measured by another and more accurate means. Otherwise, the only contributing numbers are measured angles. The final results are affected by eight recognized sources of error. Determined Refractive Index of the Glasses. T h e sixth place accuracy of these determinations, plus the effect of rounding t o the nearest unit in the fifth place, is directly transferred to the measurements of the device as a refractometer. Except for one of the prisms, it doesn't influence the anticipated results. Angle of the Prism A. This angle was measured using a good crystal goniometer. No effort was made to measure this to better than 1 minute, but this number was clearly correct, If the measurement of A were erroneous, being low by 1 minute, liquids that caused a deflection in sine of +0.1 would be interpreted as low by 0.000031 and those that caused a -0.1 deflection would be found high by 0.000035. The difference vanishes when the liquid and prism have the same index. Thus, the precision that was chosen for measuring A was barely adequate. I t should be borne in mind that an error in A includes both the prism angle and any wedge that may be introduced by a non-parallel cementing of the prism. The angle that counts is that between the surface of the coverglass (the exit surface) and the inclined edge of the prism. That between the under surface of the prism and the mounting plate will be much less important. Calibration of k, the Number That Coordinates the Sine of the Angle of Obliquity and the Micrometer Eyepiece Reading. In the present work, this comparison was performed by placing the microscope with the diaphragmed 5 X eyepiece and the 25X micrometer Klein eyepiece upon the table of a goniometer. The giant SociBtB Genevoise Goniometer/Spectrometer No. 2208, now in the NBS museum, was used for this purpose. Angle settings were made on the circle of the goniometer. These were converted to the sines of the angles and the coefficient relating the sine of obliquity and the scale reading averaged for insertion into the equations from which h was computed. Backlash in Micrometer Eyepiece. Since the measuring eyepiece is 25X whereas most eyepieces of this type are lox,a failure in coordination between the reading on the scale and the actual deviation is more persistent than one might anticipate. Repeated settings may become variable because of backlash. When this happens, it is necessary to take the eyepiece apart and re-lubricate the screw and particularly the ways. Since 0.3 of a scale reading is equivalent to about 0.00001in index, the sensitive nature of this problem is apparent. Apparently, it is not necessary to increase the coerciveness of the springs although this was first tried as a remedy. Human Errors in Setting the Micrometer. The entire operation is carried out a t nearly the limiting resolving power of an optical instrument of the working aperture as limited by the projected area of the prism end. Clearly, the setting must be made with all possible care. The observer must have good eyes-steady, low in corneal irregularities, and nearly free from refractive inhomogeneities in the lens and especially the vitreous humor. It is important for him to test his consistency with a series of readings under the same conditions. It may be pointed out that it is hard to make these settings by placing a line in the eyepiece over a
Table I. Refractive Properties of the Eight Prisms at 20 "C Prism
0.6563 urn
0.5893 urna
0.4861 um
1.45639 1.52104 1.57001 1.61614 1.6425 1 1.69316
1.45845 1.52375 1.57296 1.62064 1.64793 1.69972 1.741~~ 1.78330
1.46319 1.52992 1.58000 1.63287 1,66169 1.71575
1.77484 a
1.80487
Anqle of prism
59" 49' 72" 4' 72" 6' 72" 8' 72" 4' 72" 2' 72" 7' 72" 5'
Intensity weighted mean of sodium doublet D1,Dz.
similar parallel line from the light source. Diffraction artifacts confuse the image and make it so that settings appear equally satisfactory over much more than the theoretical range. The end of one line against the opposing end of another line is fairly satisfactory. A line in one against a 45' cross in the other is somewhat less good, the diffraction artifacts becoming prominent a t the crossover. A nearly perfect system is provided by a dark line a t the source and a slightly bright line in the eyepiece that is about twice as wide as the image of the dark line. This is served well by about 80 to 90% transmission in darkened part, made either by evaporating a neutral colored metal (for example, nichrome) t o cover all but a single protected line with about a 10-20% absorbing film or by evaporating the metal, removing the line with a diamond tool, and then mounting a coverglass with a setting or congealing cement that has a refractive index to match the index of the glass. Shifts of Optical Element from the Position at Which k Has Been Determined. The source marker (the target) is a t nominal infinity. This is achieved by having it a t the focus of a lens. If the position is incorrect, the image a t the exit pupil of the 5 X eyepiece (the focus of the filar micrometer 25X eyepiece) will be moved in the same direction. The coefficient connecting scale reading with sine of displacement will be altered. I t has seemed advisable to establish a fixed distance between each of the following: target and collimating lens, microscope objective and eyepiece, field lens and eye lens of the ocular, ocular and reference marker. I t is good to stabilize these distances by drilling holes and inserting removable pins. Precise controls of other distances, e.g., collimater lens to cell, and the reference marker to eye lens are less critical. This last setting is adjusted to fit the spontaneous focus position of the observer but does not alter the relation between deflection and distance a t the eyepiece. Collimater to cell distance is not critical: cell to objective distance needs to be controlled only so that an image of the prism will form a t the diaphragm plane of the eyepiece. Temperature of Liquid. Most liquids decrease in refractive index about 50 units in the fifth place with every degree rise in temperature. I t is necessary, therefore, to know the temperature to better than h0.02 O C . The devices described here are not well suited to enclosure in thermostats or the insertion of temperature control devices. Unless such control devices are sophisticated, depending upon a measurement of ambient conditions and proportional modifications, they may simply substitute cyclic variations for the changes they are intended to correct. Fortunately, good and continuing knowledge of a steady or uniformly drifting room temperature may in many instances provide enough information. The temperature of the fluid in a cell of this design changes in the direction of room temperature so that the difference is halved approximately every 2.8 ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
1119
minutes. If room temperature at the spot where the apparatus is set up changes at a rate less than 1 "C per hour for five minutes or more, the actual temperature in the cell can be satisfactorily evaluated. Such stability of a spot in the room may not always be available. In such event, a large bucket or small tub of water, nearly at room temperature, will hold a sufficiently steady temperature. A small can holding dichlorodifluoromethane or 1,2-dichlorotetrafluoroethane refrigerant is kept under the water. If the gas from the opened valve of the can escapes through two capillary throttles under the water, is then led through the tubing under the water level and impinged upon the cell from top and bottom through two large hypodermic needles (e.g. 14 gauge), the temperature of the cell will be nearly the same as that of the tank. Some Joule-Thomson cooling is theoretically present, but because the capillary throttles are under water and the needles much larger than the capillaries, the effect is small. The temperature should be within a degree of that at which the index of the prism was measured. If the liquid being measured is rapidly volatile, the chamber must be closed to prevent evaporative cooling. Temperature Coefficient of the Glass Prisms. The optical glasses change in refractive index from about 2 X 10-6 per degree for the lower crown glasses to 6 X or more for the more refractive flint glasses. That of fused quartz is anomalously large, being about 1 x per degree ( 1 3 ) . The changes are not completely predictable on the basis of refractive index. This must be borne in mind. It particularly influences the choice of room temperature at which experiments are performed.
INDEPENDENT EVIDENCE OF ACCURACY Eight unrelated sources of possible error have been described. Two and possibly three of these introduce uncertainties that are individually almost as large as the desired uncertainty. This leaves the question of whether the overall accuracy of the instrument as completed is as good as had been planned. The question is not easily answered. Standard reference materials as issued by NBS or the American Petroleum Institute and certified for refractive index have marginal value. The n ~ ~ O for . 0 2,2,4-trimethylpentane is listed by NBS as 1.39147 f 0.00002 and based on measurements made before 1950. The best API materials are now listed as having an uncertainty of three in the fifth place. These are based, however, on determinations in NBS laboratories more than a quarter of a century ago. Such reference materials have only marginal value so far as present purposes are concerned. Their own uncertainty is as great as the discrepancy in comparison. Measurements of refractive index on 1,2-dichlorobenzene and 1,2-dibromobenzene as recorded would be entirely satisfactory for our use, but the criteria of attained purity and methods of purification as reported by von Auwers and Fruhling (14) were inadequate. A number of inorganic solids can serve as good tests for the reason that purity is no problem and because the refractive index is known with sufficient accuracy. Thus, sodium chloride as halite from certain New York state mines
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is pure by all tests and has a refractive index at 20 "C for the weighted sodium lines (0.58929 pm) of 1.54433. The temperature coefficient is high, being approximately half that of matching liquids, but this can be corrected. Calcium carbonate as iceland spar has an "ordinary" index of 1.65836 at the same temperature and wavelength. The "ordinary" index of silicon dioxide as clear crystalline quartz is 1.544246. The solids cannot be compared directly. They can, however, be matched with liquids. In this case, the desired accuracy of match can be achieved only by bracketing-mixing liquids until, by the phase-contrast principle, there is the least perceptible difference in index between liquid and crystal and determining the nominal index of the liquid. The liquid composition is then changed until there is the opposite least observable difference. The average of index of the two liquid mixtures will not differ from the true index of the crystal by as much as This process is awkward, painstaking, but it does confirm that, on those days when one's eyesight is good and nerves are steady, the final error of the refractive index determination as the average of 5 separate measurements does not normally exceed 0.00001. Another test is the self-contained one. Each prism overlaps the range of the two adjacent prisms. The anticipated errors of each are greatest in these parts of their range and each comparison involves two errors. Except in the case of tests utilizing prisms 1 and 7 which were themselves dependent on intercomparisons, this procedure approximately sustains the concept that errors are very small in the fifth place. The amount of sample required is about 1 cubic millimeter. To achieve this small amount, it is necessary to introduce an auxiliary dam that will lie between the top and bottom windows and face the prism. The liquid is then held by capillarity. Unused waste prisms from the assembly of the cell are perfectly suited to this purpose.
LITERATURE CITED (1) C. P. Saylor, "The Characterization of Chemical Purity." L. Stavely, Ed., published for International Union of Pure and Applied Chemistry by Butterworth and Company, London, 1971, p 67. (2) S. M. Ojena and P. R. DeForest, J. Forensic Sci. SOC., 12, 315 (1972) and J. Forensic Sci., 17, 409 (1972). (3) M.-F. d'Albert d'Ailly. le Duc de Chaulnes, "Histoire de I'Academie Royal des Science," for 1767, pp 163-175, and Mem. Math. Phys., l'Acad. Roy. Sci. for 1767, pp 431-433, Paris, 1770. (4) Albert Johannsen. "Manual of Petrographic Methods," Wiley, New York, 1914, et seq. (5) F. E. Wright, J. Wash. Acad. Sci., 4, 269 (1914). (6) L. Nichols, Nat. Paint&//., 1, 12 and 14 (1937). (7) K. L. Alber and J. T. Bryant, hd. Eng. Chem., Anal. Ed., 12, 305 (1940). (8) B. A. Brice and R. Speiser, J. Opt. SOC.Am., 36, 363A (1956); and B. A. Brice and M. Halwer, J. Opt. SOC.Am., 41, 1033 (1951). (9) P. P. Debye, J. Appl. Phys., 17, 392 (1946). (10) E. E. Jeiiey. J. R. Microsc. Soc., 54, 234 (1934). (11) C. P. Saylor, Adv. Opt. Electron Microsc., 1, 57 (1966). (12) /bid., p 64. (13) I. H. Malitson, J. Opt. SOC.Am., 55, 1205 (1965). (14) K. von Auwers and A. Fruhling, Justus Liebig's Ann. Chem., 422, 160 (1921).
RECEIVEDfor review September 30, 1974. Accepted December 4,1975.
