Abstract

A new method for measuring the refractive index of liquid, proposed in a previous paper [Appl. Opt. 36, 5552–5556 (1997)], has been developed. The minimum deviation of a laser beam deflected by a liquid-filled cylindrical cell was calculated by use of geometric optics. These theoretical results were compared with experimental results, with excellent agreement. As a result, the unknown refractive index of a liquid could be obtained by use of a computer calculation to give a best fit. The computer calculation showed that the sensitivity of the refractometer increases with the cell-wall thickness until total reflection takes place. A small refractive-index difference can be detected within a precision of 1 × 10-6 by use of a metal-oxide semiconductor linear image sensor. We show how to calibrate the refractometer with pure water at 3.98 °C.

© 1998 Optical Society of America

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References

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  1. H. Hattori, H. Yamanaka, H. Kurniawan, S. Yokoi, K. Kagawa, “Using minimum deviation of a secondary rainbow and its application to water analysis in a high-precision, refractive-index comparator for liquids,” Appl. Opt. 36, 5552–5556 (1997).
    [CrossRef] [PubMed]
  2. S. Svanberg, Atomic and Molecular Spectroscopy, 2nd ed. (Springer-Verlag, New York, 1992).
    [CrossRef]
  3. D. K. Lynch, W. Livingstone, Color and Light in Nature (Cambridge U. Press, London, 1995).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  12. C. A. Faick, B. Fonoruff, “A precision apparatus for the rapid determination of indices of refraction and dispersion by immersion,” J. Res. Natl. Bur. Stand. USA 32, 67–75 (1944).
    [CrossRef]
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  16. Chemical Society of Japan , ed., Table for Chemistry, (Maruzen, Tokyo, 1966).

1997

1991

1971

1968

1952

E. C. Miller, F. W. Crawford, B. J. Simmons, “A differential refractometer for process control,” Anal. Chem. 24, 1087–1090 (1952).
[CrossRef]

1951

1944

C. A. Faick, B. Fonoruff, “A precision apparatus for the rapid determination of indices of refraction and dispersion by immersion,” J. Res. Natl. Bur. Stand. USA 32, 67–75 (1944).
[CrossRef]

1941

J. V. Hughes, “A new precision refractometer,” J. Sci. Instrum. 18, 234–237 (1941).
[CrossRef]

Brice, Z. B. A.

Crawford, F. W.

E. C. Miller, F. W. Crawford, B. J. Simmons, “A differential refractometer for process control,” Anal. Chem. 24, 1087–1090 (1952).
[CrossRef]

Faick, C. A.

C. A. Faick, B. Fonoruff, “A precision apparatus for the rapid determination of indices of refraction and dispersion by immersion,” J. Res. Natl. Bur. Stand. USA 32, 67–75 (1944).
[CrossRef]

Fichter, G. E.

G. E. Fichter, Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, New York, 1967), Vol. 4, p. 363.

Fonoruff, B.

C. A. Faick, B. Fonoruff, “A precision apparatus for the rapid determination of indices of refraction and dispersion by immersion,” J. Res. Natl. Bur. Stand. USA 32, 67–75 (1944).
[CrossRef]

Gunter, R. C.

Halwer, M.

Hattori, H.

Hecht, E.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).

Hughes, J. V.

J. V. Hughes, “A new precision refractometer,” J. Sci. Instrum. 18, 234–237 (1941).
[CrossRef]

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976).

Kagawa, K.

Kessler, H.

H. Kessler, Handbuch der Physik, H. Geiger, K. Schcel, eds. (Springer-Verlag, Berlin, 1927).

Kobeissi, M. A.

Kurniawan, H.

Livingstone, W.

D. K. Lynch, W. Livingstone, Color and Light in Nature (Cambridge U. Press, London, 1995).

Lynch, D. K.

D. K. Lynch, P. Schwartz, “Rainbows and fogbows,” Appl. Opt. 30, 3415–3420 (1991).
[CrossRef] [PubMed]

D. K. Lynch, W. Livingstone, Color and Light in Nature (Cambridge U. Press, London, 1995).

Miller, E. C.

E. C. Miller, F. W. Crawford, B. J. Simmons, “A differential refractometer for process control,” Anal. Chem. 24, 1087–1090 (1952).
[CrossRef]

Schwartz, P.

Simmons, B. J.

E. C. Miller, F. W. Crawford, B. J. Simmons, “A differential refractometer for process control,” Anal. Chem. 24, 1087–1090 (1952).
[CrossRef]

Svanberg, S.

S. Svanberg, Atomic and Molecular Spectroscopy, 2nd ed. (Springer-Verlag, New York, 1992).
[CrossRef]

Werner, A. J.

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976).

Yamanaka, H.

Yokoi, S.

Yoshinage, H.

H. Yoshinage, Handbook of Applied Spectroscopy (Asakura, Tokyo, Japan, 1973).

Anal. Chem.

E. C. Miller, F. W. Crawford, B. J. Simmons, “A differential refractometer for process control,” Anal. Chem. 24, 1087–1090 (1952).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

J. Res. Natl. Bur. Stand. USA

C. A. Faick, B. Fonoruff, “A precision apparatus for the rapid determination of indices of refraction and dispersion by immersion,” J. Res. Natl. Bur. Stand. USA 32, 67–75 (1944).
[CrossRef]

J. Sci. Instrum.

J. V. Hughes, “A new precision refractometer,” J. Sci. Instrum. 18, 234–237 (1941).
[CrossRef]

Other

S. Svanberg, Atomic and Molecular Spectroscopy, 2nd ed. (Springer-Verlag, New York, 1992).
[CrossRef]

D. K. Lynch, W. Livingstone, Color and Light in Nature (Cambridge U. Press, London, 1995).

H. Yoshinage, Handbook of Applied Spectroscopy (Asakura, Tokyo, Japan, 1973).

Chemical Society of Japan , ed., Table for Chemistry, (Maruzen, Tokyo, 1966).

H. Kessler, Handbuch der Physik, H. Geiger, K. Schcel, eds. (Springer-Verlag, Berlin, 1927).

G. E. Fichter, Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, New York, 1967), Vol. 4, p. 363.

F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976).

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).

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Figures (8)

Fig. 1
Fig. 1

Diagram showing the optical ray traversing a cylindrical cell containing water.

Fig. 2
Fig. 2

Theoretical result of the relationship between the refractive index of a liquid, n 2, and the difference of minimum deviation angle, θ m , in degrees. The calculation was done for the second-order minimum deviation on a wavelength of 543.5 nm.

Fig. 3
Fig. 3

Theoretical results of the relationship between the refractive index of liquid and the difference of the minimum deviation angle, θ m , in degrees, for three thicknesses of the cell: 2, 5, and 7 mm.

Fig. 4
Fig. 4

Examples of the interference fringe observed at the minimum deviation. (a) Second-order minimum deviation, (b) seventh-order minimum deviation. These were obtained with 543.5-nm He–Ne laser light.

Fig. 5
Fig. 5

Comparison of the enlarged interference fringes taken at the two water temperatures shown.

Fig. 6
Fig. 6

Relationship between the displacement length of the interference fringe position and the temperature of pure water. UV Laser, G Laser, and R Laser: He–Cd, He–Ne, and He–Ne, respectively, at the wavelengths listed. Fringes of the second-order minimum deviation and of the seventh-order minimum deviation were used.

Fig. 7
Fig. 7

Relationship between the displacement length of the second-order fringe position and the concentration of sugar in water for three lasers.

Fig. 8
Fig. 8

Relationship between the displacement length of the second-order fringe position and the concentration of an agricultural chemical for two lasers.

Tables (4)

Tables Icon

Table 1 Minimum Deviation Angle θ (in degrees) for Various Orders Pa

Tables Icon

Table 2 Sensitivity of the Refractometer for Various Cell Thicknesses

Tables Icon

Table 3 Minimum Deviation Angle (in degrees) for Various Orders

Tables Icon

Table 4 Minimum Deviation Angle (in degrees) for Various Orders

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

θ = A - B + C - D + C - D + π - 2 B + C - D + C - D + A - B = 2 A - B + 4 C - D + π - 2 B .
θ = 2 A - B + 2 P + 1 C - D + P π - 2 B ,
B = sin - 1 sin   A / n 1 .
y - R   sin   A = tan B - A X + R   cos   A .
x 2 + y 2 = r 2 .
x Q 2 = - b - d 1 / 2 / 2 a ,
a = 1 + tan 2 B - A , b = 2 R   tan B - A cos   A   tan B - A + sin   A , c = R 2 cos   A   tan B - A cos   A   tan B - A + 2   sin   A + R 2 sin 2   A - r 2 , d = b 2 - 4 ac .
A = cos - 1 - x Q 2 / r ,
C = B + A - A .
D = sin - 1 n 1 sin   C / n 2 .

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