Seiji NAKAMURA and Asakazu MURAMOTO.

Transcription

1 A Liquid Refractometer. BY Seiji NAKAMURA and Asakazu MURAMOTO. [Brain Nov. 19, 1921.] Abstract. The theory and description of a refractmeter for a liquid arc given. The principle of the instrument is to find the index from the measurement of the fecal length of a liquid lens. The liquid to be tested is placed in a narrow space confined between a glass lens and a plane mirror. A brightly illuminated object is placed before the system and the real image reflected from the system is formed. The image is made to coincide with the object by using an auto-collimating ocular. Such arrangements were already described by several authors but they have all drawback that the reduction formula is not quite simple, and that the index of refraction of glass enters into the expression. The writers show how by taking an equicurved concavo-convex lens, the index of the lens is made to disappear from the formula, and thus it furnishes us a method of absolute determination of the index The method of measuring the index of refraction of a liquid from the determination of the focal length of a liquid lens is not new, being first suggested by Blakesley(l) and by Pingriff(2). The arrangements proposed by Nettlelon(3) and by Dawes(4), however, have the drawback that firstly the formula for the reduction is not simple and secondly that it is a relative measurement, so that they are rather laboratory experiments destined for exercise of students. The advantage of the following arrangemcnt is its simplicity of the formula and its giving us a method of absolute determination. Principle. In Fig. 1,let M be a plane mirror and L a lens, whose axis is perpendicular to the phone of the mirror, and Q a liquid interposed between them. At F is placed a strongly illmcinated object, and Oc is an auto-collinmting Fig. 1. ocular. If the system consisting of F and Oc be noved along the axis (1) T.H. Blakesley, I'roc. Opt, Convention, No. 1 (11905), 189) (2) G.N. Pingriff, Nature, 87 (7011), 551. (3) H.R. Nettleton, Proc. Phys. Soc. London, 23 (1915), 511 (4) H.F., Dawes Phys. Rev., 26 (1915), 354.

2 4 S. NAKAMURAND A. MURAMOTO: [Ser. 3, Vol. 4 of the lens until the image of F reflected from the minor coincides with the object, then we have the position of auto-collimation. If N and n be the indices of refraction of the lens and the liquid respectively, and r, s be the radii of curvature of the lens supposed to be double convex, then it can be shown that at the position of the auto-collimation, the distance v of the object from the front vertex A of the lens satisfies the relation where d is the axial thickness of the lens. So that if we know N, r, s, and d, we can determine n from the measurement of v. Simplification. So far the method is relative, as the value of n depends on N. The essential difference of the present arrangement from the former ones is the great simplification caused by taking an equicurved concavoconvex lens, i. e. by making r= -s, then we have As the second term is usualy very small, we may neglect it, and we may determine n by the following simple relation Thus we need not know the index of refraction of lens, and the arrangement has a great advantage of being a method of the absolute determination of n. This peculiarity recommends it to the study of the variation of n with temperature, which is rather troublesome in relative instruments as Pulfrich's or Abbe's refractometers. In order to study the effect of the second term, let us take a case of the instrument made by us, in which s = mm., and d = 5 mm., with N = As the mange of n lies between 1 3 and 1 7 in usual liquids let us take values of v giving n lying between these limits. Calculate the approximate values of n corresponding to these assumed values of v, and then the values of the second term are calculated. These values are given in the accompanying table. In the same table, the difference of the values of 1/* due to a difference of 1 mm. in v are given, and they show at once that the effect of the second term is usually less than the effects of the error of 1 mm. in the measurement of v. As a difference of 1 mm. in the reading of causes a difference of n amount0ing respectively to and,

3 Jan 1922.] A LIQUID REFRACTMETER for v=250mm. and 650 mm., if the accuracy required for n is to the third decimal place, as in the case when the dispersion is neglected, we may safely neglect the second term. If the accuracy re quired for n is greater and if it is thought necessary to take the second term into the consideration, then we may proceed as follows. Suppose that we apply a correction to the observed distance v, which enables us to use the simple formula without the second term. Let the corrected distance be v', then or but by (2) therefore The values of are given in the last column of the above table. They show how insignificant such correction usually is. And as any small variation in the value of N does not cause any material change in this method

4 6 5. NAKAMURA AND A. MURAMOTO : [Ser. 3, Vol. 4 may be used to the study of the variation of 92 with temperature as before, and also to the study of the dispersion of the liquid. Lens and liquid holder. k metal frame 1 much like a photographic printing frame mounted on a circular stage with tripods 2 served as the lens and liquid holder. The lens 3 is cemented with its axis firmly within a circular hole bored in a wall of the frame. The periphery of the lens on its concave side is ground for a breadth of about 1 mm. to bring it in one plane with the inner wall of the frame, so that when the lens is held horizontally and a small quantity of the liquid to be tested is put on the concavity of the lens and then covered with a silvered glass miror 4 kept in its place with a metal plate 5 and a spring 6, then the liquid is held in the space between the lens and the mirror by its capillarity, even when the lens is erected. The mirror must be applied to the lens with its silvered side away from the liquid, for otherwise the reflected image from liquid-silver bound:cry is very faint and extremely diffieult to observe. This lens holder is put on one end of an optical bench about SO c m. long with its tripods resting on the three V-shaped canals 7. Observing system. The auto-collimating ocular S is of usual Ramsden type with a pretty long focal length. Behind it a right angled reflecting prism 9 is mounted in such a way that the observer ran look perpendicular to the length of the optical bench and seek for the image of an object placed at the focus of the ocular at his great case. The object 111 is a scale engraved on a glass plate, and the position of the Fig. 2. system is sought for the exact equality of the image and the object. Another alternative arrangement, which was found to be satisfactory, was a scale placed in such a way that its middle point was at the focus of the ocular its length making an angle of about fourty or fifty degrees with the line of sight, If we look such scale through the ocular, some narrow region near the focus can only be clearly seen, so that the ocular can be, brought to focus sharply a definite line of the scale. The real image of the scale is so inclined, but to the opposite side, so that by rnoving the observing al system along the bench we can accurately focus and bring the reflected image of the particular line to coincide with the object. For guiding the moving system along the bench, we used a mechanical

5 Jan ] A LIQUID REFRACTMETER. 7 device described by Whipple, (1) and found to work very smoothly- The device consists of a circular cylinder 11 running parallel to the bench and a plane 12 fixed to the bench, and two V's and a point are attached to the moving system. These V's are made to slide on the cylinder, and the point on the plane, thus there are five points at which the moving systern is in contact with the bench, leaving only one freedom of translation along the bench. (1) R.S. Whipple, Trans. Opt. Soc. London, 22 (1920), 41.