METHOD for the DETERMINATION of the INDICES of REFRACTION Of LIQUIDS JOHN L. SHELDON Battle Creek College, Battle Creek, Michigan
A simple, inexpensive device for the determination of 1 1 1 (n-1) (1) ~ + F - 1p F = ~ the refractive indices of liquids is described. This consists of a hollow plano-convex lens,formed by a PlmofocW ~tis pointed out by Gladden that when a liquid of low meniscus sfictacle lens and a me7 'glass. A short viscosity, such as water, is employed +ibrations incimethod for the use of the dmice is outliwd. Results dental to focusing make it difficult to obtain an exact showing the degree of accuracy attainable are presented. focus. In the case of water, mors of as much as one ++++++ centimeter in the determination of the image distance may result. N A RECENT number of the Rtvim of Scientific In making some preliminary trials by this method the Instruments Gladden1 has described a simple, inexpensive method for the determination of in- author of the present article measured the radii of m a dices of refraction of liquids by students. Bridy, the ture of several dozen watch glasses and found the method consists of placing the liquid in an ordinary curvatures of all varied considerably from place to watch glass, which gives the liquid the form of a plano- place. Two of the best were selected for trial. I t was convex lens. The -elass.. coutainine the liauid, is held found that the non-uniformity of curvature resulted in by a lens holder attached to a verti&ly supported two- vTPoor image formation, even in the absence of it was found that unless a diaphragm meter optical bench. The trademark on a Mazda bulb vibtlrtion. and image were used the irregularity of the edges of the liquid is then focused on a sneen and the surface resulted in further degradation of the image. distances, a and b, are measured. l-he radius of ture., R., is measured with a s~herometerand the index Using a two-meter optical bench vertically was also somewhat objectionable. of refraction, n,is calculated by the equation: While attempting to improve upon the method an'GLADDBN, S. C., "A simple method of determining the re- other device was evolved which is inexpensive, costing fractive index of liquids." Rev. of Sci. Instruments. 4, 231 (April. about one dollar to make, and which has practically 1933).
I
a
.
none of the objectionable features of the above-described method. I t consists of two parts, a thin, plano focus, meniscus lens and a cover slip, as shown in Fimtre 1.
The lens was ground by a local optical shop. The curvatures of the two sides are equal, but opposite in sign, being 7 diopters. I t has a diameter of 50 mm., although a smaller diameter would probably do as well. I t also has a flat rim, which, as will be seen in Figure 3, makes contact with the cover glass. The rim was ground as follows. il small amount of- fine valvegrinding compound was thinly spread on a piece of old plate glass. After cleaning the hands the lens was placed on the glass, concave side down, and then moved about in all directions, with simultaneous application of very light pressure. Care was taken not to scratch the lens. This was continued until a rim about 1.5-2 mm. in width was formed.
parts are held in one hand, as shown in Figure 2. The lens is held tightly to the under side of the cover glass with the fingers, the lens projecting slightly beyond the edge of the cover. Liquids may be introduced by means of a small pipet or by pouring directly from the bottle. The open paxt is elevated slightly so that bubbles may escape. By careful pouring slightly more than enough liquid to fill the lens will be held in place by surface tension. With one movement of the fingers the cover is slid over the open part, the lens then being completely filled and free from air bubbles. The lens, still on the lower side, is then centered more carefully with both hands and the excess liquid is wiped off with a lintless rag. The two parts will then hold tightly together, the same as two pieces of glass with liquid between, and may be placed in the lens holder of an optical bench, as shown in Figure 3. The lens was , always used on the same side of the cover, that side being identified by a beveled top edge. Also, by means of a small scratch on the outside edge of the lens and a similar one in the middle of the upper edge oi the co\vr, it was possibk alwsvs to place the lrns in the sanw inxition on the cover. \'olatilc liquids, snch as c:irbon disulfide a n d Frcnne :j ether, leak slowly, forming a small air bubble at the top of the lens. In an attempt to stop this, one side of the cover glass was polished by an optician on a plano lap to remove any slight irregularities. This did not seem to make any great difference. It is believed that careful selection of the piece of glass for the cover and the grinding of the rim on the lens with fine compound will result in a minimum of leakage. In any event the bubble that slowly forms at the top does not interfere with the use of the lens. The two liquids mentioned and ethyl acetate were the only ones of those investi~ a t e dwhich leaked. The optical bench, which was one meter in length, had three slides, one for an object screen, one for the lens holder, and one for an image screen. The object screen was illuminated from behind by a sodium flame (a small piece of fused sodium chloride on the screen of a Meker burner). When the object and image screens and the lens in the holder were once aligned they were not disturbed again, the only further adjustments con0
I'rocnc 2
The cover glass, which is 5-6 mm. wider than the lens, was cut from a piece of selected lantern slide cover glass with a sharp glass cutter and the edges were smoothed with a fine abrasive stone. When the two parts are placed together a hollow, plano-convex lens is formed. To fill the lens the two
sisting of removal and replacement of the lens and ad- being equal. Then the image distance was determined justment of the positions of the object and image slides carefully six times and these values were averaged. on the bench. TABLE 2 Adjustments were made so that the front of the conBeazsas-Roolr TerPEaiirvas 25-C b vex surface, which faced the image screen, should be 31.20 directly over the middle (50 cm. mark) of the optical 31.20 bench in order that measurements of object and 31.20 31.20 image distances could be made from that ~ u r f a c e . ~ 3120 The usual procedure for measuring the focal length 31.20 of a thin lens3 is to place the object a t various points Average 31.20 along the optical bench, focus the image sharply, and It was believed that less error would be introduced in measure the corresponding object and image distances, a and b. Several sets of values are obtained and the determining the index of refraction if the radius of values for F, calculated by means of Equation (I), are curvature were determined indirectly rather than by direct measurement. Accordingly, distilled water was averaged. In order that the measurements of the focal lengths of used as a reference liquid, the focal length of the lens the various liquid lenses might he made under similar 94.40 conditions, the object was placed in each case so that a was approximately equal to b. Several settings of the 1 94.30 object were made, but in each case a did not differ from b by more than approximately 2 cm. Table 1shows the complete data for one liquid. z94.20
8
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TABLE 1 B~~zawe-25~C. D~violianin Dh./1000 of ihc ad~'rsgf b which were aml.o#ed ,a sivc lhr v d u c ohown
No, of Rcodings Awowd 6 4 6 3
a 30.00 31.00 31.20 32.00
b 32.49 31.36 31.20 30.47
F 15.60 15.59 15.60 16.61
Mnr. Dau.
6.2 1.6 2.6 0.7
Mcon Dm. 1.4 0.6 1.0 0.6
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While quite accurate results were obtained, yet considerable time was required when several settings of the object distance were made. Therefore, a short method was worked out, which also involves a minimum of calculation. When either the object or image distance, a or b, is plotted against the total distance from object to image, a b, a curve like that in Figure 4 is obtained. It will be seen that the curve passes thiough a minimum and it can be shown that this minimum+xcurs when a = b. Now when a = b,
+
Therefore, when a = b the focal length is obtained by dividing the total object-image distance by 4. Further inspection of the curve shows it to be quite flat a t the minimum and that a can differfrom b by as much as one centimeter and the focal length, as determined by dividinp. a b by 4, will be practically the same as when ais equal to b. This method was used for determining the indices of refraction of a number of liauids. Bv trial and error the object and image distances were adjusted until approximately equal. It did not require more than one or two minutes to get them within 1-2 mm. of
+
94.10
m
g94.00
i
+.
2 93.90 w
3
-
O 93.80
+
93.70 44
45 46 47 48.' 49 Object Distance - (6) - cm. FIGURE4
50
,
containing water being determined accurately and the radius of calculated from the known index of refraction of water a t the room temperature by use of equation (3). a+b
4
- F= R n-1
(3)
The focal length of the lens containing water was measured more than once, a t different times and on different days. These values are given in Table 3. TABLE 3
Room Tmmplroiurr 25°C.
23 25 26 25
Focd Length 23.17 23.14 23.15 23.20 23.18
Knowing the radius of curvature, the index of refraction of another liquid is calculated by useof equation (4).
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MINOR, R. S.. "Physical measurements." published by the author, Berkeley, California, 1925, Parts 111 and IV, p. 91. WMOR, R.S., bc. d.,p. 93.
~h~ indices of refraction of the first eleven liquids in Table 4 were determined in 90 minutes. The entire
The maximum error (carbon disulfide) was 3.7 parts/1000. The average error for the 17 liquids was 1part/1000. It will be seen from Tables 3 and 4 that whiie this TABLE 4 short method is simple, yet it gives results that are INDICBS 01 RBIIRACI~ON &T 23'C.. SODIOY L I O ~ fairly consistent and accurate. The lack of exact " 7, Liguid (Exparimanld) Landoll-Bansf&* temperature control is of course a weak point, but n-Rprp~lalcohol 1.385 1.384 probably does not introduce errors greater than those iso-Ropy1 nl~ohol 1.376 1.376 already inherent in the technic. n-Bufyl alcohol 1.398 1.398 Ethyl bromide 1.420 1.422 The method should find application in the student Carbon tetrachloride 1.458 1.458 Carbon dirulfide 1.620 1.626 physical chemistry laboratory where a refractometer is 1.494 1.484 Toluene not available. The lens is cheap and an occasional Benmldehyde 1.543 1.545 1.585 1.584 Aniline breakage is not serious. Experimentally determined Nitrobenzene 1.553 1.552 molar and atomic indices of refraction compare very ... Methyl ralieylnte 1.536 1.494 1.499 Benzene with accepted values and a sufficient number of well Methyl alcohol 1 321 1.328 liquids may be run in the usual laboratory period. 1.358 1.357 Acetone Ethyl acetate 1.368 1.372 In the organic laboratory the indices of refraction of 1.350 1.351 Ether 1.371 1.370 liquids may be determined for the purpose of partial Acetic acid * LANDOLT-BORNSTEIN, "Physikalisdl-cbemiSche Tabellen," identification. In the student physics laboratory indices of refraction 1923, Vol. 11,pp. 968-82. Tabulated values were recalculated to 23'C. by means of the values given for dnldt on pp. 9834. of liquids may be determined in connection with other In the few instances in which these values are not given average experiments using the optical bench. values for compounds of the same type were used. seventeen liquids required only two hours, during which time water was run three t i e s as a check, at the beginning and end and once in between.
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