Abstract

The refractive index of a liquid is determined with 0.0003 accuracy from measurements of laser beam displacement by a liquid-filled standard 10mm spectrophotometer cell. The apparatus and methods are described and the results of measurements at λ=1064nm and T=25.0°C for 30 solvents and deuterated solvents are presented. Several sources of potential systematic errors as large as 0.003 are identified, the most important being the curvature of the liquid cell windows. The measurements are analyzed accounting for the significant imperfections of the apparatus.

© 2011 Optical Society of America

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References

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    [CrossRef] [PubMed]
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  5. M. Daimon and A. Masumura, “Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region,” Appl. Opt. 46, 3811–3820 (2007).
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  6. J. Rheims, J. Koser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
    [CrossRef]
  7. G. H. Meeten, “Refractive index errors in the critical-angle and Brewster-angle mehods applied to absorbing and heterogeneous materials,” Meas. Sci. Technol. 8, 728–733 (1997).
    [CrossRef]
  8. C.-B. Kim and C. Su, “Measurement of the refractive index of liquids at 1.3 and 1.5 micron using a fibre optic Fresnel ratio meter,” Meas. Sci. Technol. 15, 1683–1686 (2004).
    [CrossRef]
  9. A. Suhadolnik, “An optical fibre interferometric refractometer,” Meas. Sci. Technol. 18, 1205–1208 (2007).
    [CrossRef]
  10. B. Santic, D. Gracin, and K. Juraic, “Measurement method for the refractive index of thick solid and liquid layers,” Appl. Opt. 48, 4430–4436 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. R. Ramponi, R. Osellame, M. Marangoni, and V. Russo, “Near-infrared refractometery of liquids by means of waveguide Cerenkov second-harmonic generation,” Appl. Opt. 37, 7737–7742 (1998).
    [CrossRef]
  13. K. G. Muller, S. Sainov, S. Mittler-Neher, and W. Knoll, “Design and test of a simple high-temperature laser microrefractometer,” Appl. Opt. 35, 708–710 (1996).
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  14. C. Bahrim and W.-T. Hsu, “Precise measurements of the refractive indices for dielectrics using an improved Brewster angle method,” Am. J. Phys. 77, 337–343 (2009).
    [CrossRef]
  15. F. El-Ghussein, J. M. Wrobel, and M. B. Kruger, “Dispersion measurements with minimum and maximum deviated beams,” Am. J. Phys. 74, 888–891 (2006).
    [CrossRef]
  16. G. E. Hassan, H. El-Kashef, B. Y. El-Baradie, and M. El-Labban, “Interferometric measurement of the physical constants of laser dye solvents,” Rev. Sci. Instrum. 66, 38–42(1995).
    [CrossRef]
  17. S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167–180 (2002).
    [CrossRef]
  18. Starna Cells catalog for typical cell specifications, at www.starnacells.com.
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    [CrossRef]
  20. Downloads for Spectrosil and Quartz Glass for Optics: Data and Properties, at http://heraeus-quarzglas.com.
  21. CRC Handbook of Chemistry and Physics, 68th ed., R.C.Weast, ed. (CRC, 1987).
  22. S. Qin, A. Huang, and X. Wang, “Optical angular encoder installation error measurement and calibration by ring laser gyroscope,” IEEE Trans. Instrum. Meas. 59, 506–511(2010).
    [CrossRef]
  23. A. Samoc, “Dispersion of refractive properties of solvents: chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94, 6167–6174(2003).
    [CrossRef]
  24. D. Beysens and P. Calmettes, “Temperature dependence of the refractive indices of liquids: deviation from the Lorentz–Lorenz formula,” J. Chem. Phys. 66, 766–771 (1977).
    [CrossRef]
  25. M. Debenham and G. D. Dew, “The refractive index of toluene in the visible spectral region,” J. Phys. E 14, 544–545 (1981).
    [CrossRef]
  26. S. Valkai, J. Liszi, and I. Szalai, “Temperature dependence of the refractive index for three chloromethane liquids at 514.5 nm and 632.8 nm wavelengths,” J. Chem. Thermodyn. 30, 825–832 (1998).
    [CrossRef]

2010 (2)

D. P. Shelton, “Nonlocal hyper-Rayleigh scattering from liquid nitrobenzene,” J. Chem. Phys. 132, 154506 (2010).
[CrossRef] [PubMed]

S. Qin, A. Huang, and X. Wang, “Optical angular encoder installation error measurement and calibration by ring laser gyroscope,” IEEE Trans. Instrum. Meas. 59, 506–511(2010).
[CrossRef]

2009 (2)

B. Santic, D. Gracin, and K. Juraic, “Measurement method for the refractive index of thick solid and liquid layers,” Appl. Opt. 48, 4430–4436 (2009).
[CrossRef] [PubMed]

C. Bahrim and W.-T. Hsu, “Precise measurements of the refractive indices for dielectrics using an improved Brewster angle method,” Am. J. Phys. 77, 337–343 (2009).
[CrossRef]

2007 (2)

2006 (1)

F. El-Ghussein, J. M. Wrobel, and M. B. Kruger, “Dispersion measurements with minimum and maximum deviated beams,” Am. J. Phys. 74, 888–891 (2006).
[CrossRef]

2004 (1)

C.-B. Kim and C. Su, “Measurement of the refractive index of liquids at 1.3 and 1.5 micron using a fibre optic Fresnel ratio meter,” Meas. Sci. Technol. 15, 1683–1686 (2004).
[CrossRef]

2003 (1)

A. Samoc, “Dispersion of refractive properties of solvents: chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94, 6167–6174(2003).
[CrossRef]

2002 (1)

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167–180 (2002).
[CrossRef]

2001 (1)

1998 (2)

R. Ramponi, R. Osellame, M. Marangoni, and V. Russo, “Near-infrared refractometery of liquids by means of waveguide Cerenkov second-harmonic generation,” Appl. Opt. 37, 7737–7742 (1998).
[CrossRef]

S. Valkai, J. Liszi, and I. Szalai, “Temperature dependence of the refractive index for three chloromethane liquids at 514.5 nm and 632.8 nm wavelengths,” J. Chem. Thermodyn. 30, 825–832 (1998).
[CrossRef]

1997 (2)

J. Rheims, J. Koser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

G. H. Meeten, “Refractive index errors in the critical-angle and Brewster-angle mehods applied to absorbing and heterogeneous materials,” Meas. Sci. Technol. 8, 728–733 (1997).
[CrossRef]

1996 (2)

1995 (1)

G. E. Hassan, H. El-Kashef, B. Y. El-Baradie, and M. El-Labban, “Interferometric measurement of the physical constants of laser dye solvents,” Rev. Sci. Instrum. 66, 38–42(1995).
[CrossRef]

1992 (1)

1987 (1)

CRC Handbook of Chemistry and Physics, 68th ed., R.C.Weast, ed. (CRC, 1987).

1984 (1)

1981 (1)

M. Debenham and G. D. Dew, “The refractive index of toluene in the visible spectral region,” J. Phys. E 14, 544–545 (1981).
[CrossRef]

1977 (1)

D. Beysens and P. Calmettes, “Temperature dependence of the refractive indices of liquids: deviation from the Lorentz–Lorenz formula,” J. Chem. Phys. 66, 766–771 (1977).
[CrossRef]

1965 (1)

Bahrim, C.

C. Bahrim and W.-T. Hsu, “Precise measurements of the refractive indices for dielectrics using an improved Brewster angle method,” Am. J. Phys. 77, 337–343 (2009).
[CrossRef]

Beysens, D.

D. Beysens and P. Calmettes, “Temperature dependence of the refractive indices of liquids: deviation from the Lorentz–Lorenz formula,” J. Chem. Phys. 66, 766–771 (1977).
[CrossRef]

Calmettes, P.

D. Beysens and P. Calmettes, “Temperature dependence of the refractive indices of liquids: deviation from the Lorentz–Lorenz formula,” J. Chem. Phys. 66, 766–771 (1977).
[CrossRef]

Daimon, M.

de Greef, C.

Debenham, M.

M. Debenham and G. D. Dew, “The refractive index of toluene in the visible spectral region,” J. Phys. E 14, 544–545 (1981).
[CrossRef]

Dew, G. D.

M. Debenham and G. D. Dew, “The refractive index of toluene in the visible spectral region,” J. Phys. E 14, 544–545 (1981).
[CrossRef]

El-Baradie, B. Y.

G. E. Hassan, H. El-Kashef, B. Y. El-Baradie, and M. El-Labban, “Interferometric measurement of the physical constants of laser dye solvents,” Rev. Sci. Instrum. 66, 38–42(1995).
[CrossRef]

El-Ghussein, F.

F. El-Ghussein, J. M. Wrobel, and M. B. Kruger, “Dispersion measurements with minimum and maximum deviated beams,” Am. J. Phys. 74, 888–891 (2006).
[CrossRef]

El-Kashef, H.

G. E. Hassan, H. El-Kashef, B. Y. El-Baradie, and M. El-Labban, “Interferometric measurement of the physical constants of laser dye solvents,” Rev. Sci. Instrum. 66, 38–42(1995).
[CrossRef]

El-Labban, M.

G. E. Hassan, H. El-Kashef, B. Y. El-Baradie, and M. El-Labban, “Interferometric measurement of the physical constants of laser dye solvents,” Rev. Sci. Instrum. 66, 38–42(1995).
[CrossRef]

Finsy, R.

Gracin, D.

Greco, V.

Hassan, G. E.

G. E. Hassan, H. El-Kashef, B. Y. El-Baradie, and M. El-Labban, “Interferometric measurement of the physical constants of laser dye solvents,” Rev. Sci. Instrum. 66, 38–42(1995).
[CrossRef]

Hoffer, L.

Hsu, W.-T.

C. Bahrim and W.-T. Hsu, “Precise measurements of the refractive indices for dielectrics using an improved Brewster angle method,” Am. J. Phys. 77, 337–343 (2009).
[CrossRef]

Huang, A.

S. Qin, A. Huang, and X. Wang, “Optical angular encoder installation error measurement and calibration by ring laser gyroscope,” IEEE Trans. Instrum. Meas. 59, 506–511(2010).
[CrossRef]

Juraic, K.

Kim, C.-B.

C.-B. Kim and C. Su, “Measurement of the refractive index of liquids at 1.3 and 1.5 micron using a fibre optic Fresnel ratio meter,” Meas. Sci. Technol. 15, 1683–1686 (2004).
[CrossRef]

Knoll, W.

Koser, J.

J. Rheims, J. Koser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

Kruger, M. B.

F. El-Ghussein, J. M. Wrobel, and M. B. Kruger, “Dispersion measurements with minimum and maximum deviated beams,” Am. J. Phys. 74, 888–891 (2006).
[CrossRef]

Liszi, J.

S. Valkai, J. Liszi, and I. Szalai, “Temperature dependence of the refractive index for three chloromethane liquids at 514.5 nm and 632.8 nm wavelengths,” J. Chem. Thermodyn. 30, 825–832 (1998).
[CrossRef]

Malitson, I. H.

Marangoni, M.

Masumura, A.

Meeten, G. H.

G. H. Meeten, “Refractive index errors in the critical-angle and Brewster-angle mehods applied to absorbing and heterogeneous materials,” Meas. Sci. Technol. 8, 728–733 (1997).
[CrossRef]

Mittler-Neher, S.

Molesini, G.

Moreels, E.

Muller, K. G.

Nemoto, S.

Osellame, R.

Qin, S.

S. Qin, A. Huang, and X. Wang, “Optical angular encoder installation error measurement and calibration by ring laser gyroscope,” IEEE Trans. Instrum. Meas. 59, 506–511(2010).
[CrossRef]

Ramponi, R.

Rheims, J.

J. Rheims, J. Koser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

Richerzhagen, B.

Russo, V.

Sainov, S.

Samoc, A.

A. Samoc, “Dispersion of refractive properties of solvents: chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94, 6167–6174(2003).
[CrossRef]

Santic, B.

Shelton, D. P.

D. P. Shelton, “Nonlocal hyper-Rayleigh scattering from liquid nitrobenzene,” J. Chem. Phys. 132, 154506 (2010).
[CrossRef] [PubMed]

Singh, S.

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167–180 (2002).
[CrossRef]

Su, C.

C.-B. Kim and C. Su, “Measurement of the refractive index of liquids at 1.3 and 1.5 micron using a fibre optic Fresnel ratio meter,” Meas. Sci. Technol. 15, 1683–1686 (2004).
[CrossRef]

Suhadolnik, A.

A. Suhadolnik, “An optical fibre interferometric refractometer,” Meas. Sci. Technol. 18, 1205–1208 (2007).
[CrossRef]

Szalai, I.

S. Valkai, J. Liszi, and I. Szalai, “Temperature dependence of the refractive index for three chloromethane liquids at 514.5 nm and 632.8 nm wavelengths,” J. Chem. Thermodyn. 30, 825–832 (1998).
[CrossRef]

Valkai, S.

S. Valkai, J. Liszi, and I. Szalai, “Temperature dependence of the refractive index for three chloromethane liquids at 514.5 nm and 632.8 nm wavelengths,” J. Chem. Thermodyn. 30, 825–832 (1998).
[CrossRef]

Wang, X.

S. Qin, A. Huang, and X. Wang, “Optical angular encoder installation error measurement and calibration by ring laser gyroscope,” IEEE Trans. Instrum. Meas. 59, 506–511(2010).
[CrossRef]

Wriedt, T.

J. Rheims, J. Koser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

Wrobel, J. M.

F. El-Ghussein, J. M. Wrobel, and M. B. Kruger, “Dispersion measurements with minimum and maximum deviated beams,” Am. J. Phys. 74, 888–891 (2006).
[CrossRef]

Am. J. Phys. (2)

C. Bahrim and W.-T. Hsu, “Precise measurements of the refractive indices for dielectrics using an improved Brewster angle method,” Am. J. Phys. 77, 337–343 (2009).
[CrossRef]

F. El-Ghussein, J. M. Wrobel, and M. B. Kruger, “Dispersion measurements with minimum and maximum deviated beams,” Am. J. Phys. 74, 888–891 (2006).
[CrossRef]

Appl. Opt. (8)

IEEE Trans. Instrum. Meas. (1)

S. Qin, A. Huang, and X. Wang, “Optical angular encoder installation error measurement and calibration by ring laser gyroscope,” IEEE Trans. Instrum. Meas. 59, 506–511(2010).
[CrossRef]

J. Appl. Phys. (1)

A. Samoc, “Dispersion of refractive properties of solvents: chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94, 6167–6174(2003).
[CrossRef]

J. Chem. Phys. (2)

D. Beysens and P. Calmettes, “Temperature dependence of the refractive indices of liquids: deviation from the Lorentz–Lorenz formula,” J. Chem. Phys. 66, 766–771 (1977).
[CrossRef]

D. P. Shelton, “Nonlocal hyper-Rayleigh scattering from liquid nitrobenzene,” J. Chem. Phys. 132, 154506 (2010).
[CrossRef] [PubMed]

J. Chem. Thermodyn. (1)

S. Valkai, J. Liszi, and I. Szalai, “Temperature dependence of the refractive index for three chloromethane liquids at 514.5 nm and 632.8 nm wavelengths,” J. Chem. Thermodyn. 30, 825–832 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. E (1)

M. Debenham and G. D. Dew, “The refractive index of toluene in the visible spectral region,” J. Phys. E 14, 544–545 (1981).
[CrossRef]

Meas. Sci. Technol. (4)

J. Rheims, J. Koser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

G. H. Meeten, “Refractive index errors in the critical-angle and Brewster-angle mehods applied to absorbing and heterogeneous materials,” Meas. Sci. Technol. 8, 728–733 (1997).
[CrossRef]

C.-B. Kim and C. Su, “Measurement of the refractive index of liquids at 1.3 and 1.5 micron using a fibre optic Fresnel ratio meter,” Meas. Sci. Technol. 15, 1683–1686 (2004).
[CrossRef]

A. Suhadolnik, “An optical fibre interferometric refractometer,” Meas. Sci. Technol. 18, 1205–1208 (2007).
[CrossRef]

Phys. Scr. (1)

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167–180 (2002).
[CrossRef]

Rev. Sci. Instrum. (1)

G. E. Hassan, H. El-Kashef, B. Y. El-Baradie, and M. El-Labban, “Interferometric measurement of the physical constants of laser dye solvents,” Rev. Sci. Instrum. 66, 38–42(1995).
[CrossRef]

Other (3)

Starna Cells catalog for typical cell specifications, at www.starnacells.com.

Downloads for Spectrosil and Quartz Glass for Optics: Data and Properties, at http://heraeus-quarzglas.com.

CRC Handbook of Chemistry and Physics, 68th ed., R.C.Weast, ed. (CRC, 1987).

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Figures (2)

Fig. 1
Fig. 1

Schematic diagrams showing (a) the overall configuration of the apparatus viewed from above and (b)–(e) more detailed diagrams defining the parameters and variables in Table 1 and Eqs. (8, 9, 10, 11). The beam propagates right to left and the sign conventions are such that the angles θ, θ 1 , θ 12 , δ θ 12 , α 1 , and α 01 , and displacements δ, δ 2 , and x 01 are all positive as drawn.

Fig. 2
Fig. 2

(a) Beam displacement δ versus rotation angle θ for cell 1 filled with C 2 Cl 4 measured at λ = 1064 nm and T = 25.0 ° C . The open circles are the data and the solid curve is the fit to the data using the function defined by Eqs. (7, 8, 9, 10, 11, 12, 13). The value n 2 = 1.4893 ± 0.0001 is obtained from the fit. (b) The residual differences between the data and the fit for two successive sets of measurements are shown by the open and filled circles. The standard deviation for the residuals is 1.0 μm . Systematic variation of the residuals is indicated by the polynomial fit to the residuals (dashed curve).

Tables (2)

Tables Icon

Table 1 Parameters Measured for Two Sample Cells

Tables Icon

Table 2 Refractive Index n and Refractive Index Difference n H n D Between Corresponding Normal and Deuterated Liquids at λ = 1064 nm and T = 25 ° C , with the Uncertainty for the Last Digit Given in Parentheses

Equations (30)

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

Δ = d 2 sin θ [ 1 n 0 cos θ / ( n 2 2 n 0 2 sin 2 θ ) 1 / 2 ] ,
n 2 = n 0 sin θ [ 1 + cos 2 θ / ( sin θ Δ / d 2 ) 2 ] 1 / 2 .
δ 2 = d 2 sin ( δ θ 12 ) / cos ( θ 12 ) .
δ = ( d 1 + d 3 ) sin θ [ 1 n 0 cos θ / ( n 1 2 n 0 2 sin 2 θ ) 1 / 2 ] + d 2 sin θ [ 1 n 0 cos θ / ( n 2 2 n 0 2 sin 2 θ ) 1 / 2 ] .
I ( x ) = 1 + A sin K ( x x 0 ) ,
x m = ( A / K ) [ cos ( K x m K x 0 ) cos ( K D / 2 ) cos ( K x 0 ) ] .
f = δ ( θ ; n 2 , θ 0 ) + C .
x 01 = ( d 1 + d 2 / 2 ) tan θ ,
α 01 = c F x 01 ,
θ 01 = arcsin [ ( n 0 / n 1 ) sin ( θ α 01 ) ] ,
δ θ 01 = θ θ 01 α 01 ,
δ 1 = d 1 sin ( δ θ 01 ) / cos ( θ 01 ) .
x 12 = ( d 2 / 2 ) tan θ + δ 1 / cos θ ,
α 12 = c F x 12 ,
θ 12 = arcsin [ ( n 1 / n 2 ) sin ( θ 01 + α 01 α 12 α 1 ) ] ,
δ θ 12 = θ θ 12 α 12 α 1 ,
δ 2 = d 2 sin ( δ θ 12 ) / cos ( θ 12 ) .
x 23 = ( d 2 / 2 ) tan θ + ( δ 1 + δ 2 ) / cos θ ,
α 23 = c B x 23 ,
θ 23 = arcsin [ ( n 2 / n 3 ) sin ( θ 12 + α 12 α 23 α 2 ) ] ,
δ θ 23 = θ θ 23 α 23 α 1 α 2 ,
δ 3 = d 3 sin ( δ θ 23 ) / cos ( θ 23 ) .
x 34 = ( d 3 + d 2 / 2 ) tan θ + ( δ 1 + δ 2 + δ 3 ) / cos θ ,
α 34 = c B x 34 ,
θ 34 = arcsin [ ( n 3 / n 4 ) sin ( θ 23 + α 23 α 34 α 3 ) ] ,
δ θ 34 = θ θ 34 α 34 α 1 α 2 α 3 ,
L 4 = d 4 + ( d 3 + d 2 / 2 ) ( 1 1 / cos θ ) + ( δ 1 + δ 2 + δ 3 ) tan θ ,
δ 4 = L 4 tan ( δ θ 34 ) .
δ ( θ ) = δ 1 + δ 2 + δ 3 + δ 4 .
θ m = θ m + E [ sin ( θ m + ϕ E ) sin ( ϕ E ) ] ,

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