Abstract

A simple method for measuring the refractive index of liquid is presented. When a laser beam impinges obliquely on a rectangular cell filled with liquid and passes through the cell, the propagation axis of the transmitted beam is displaced from that of the incident beam. By measuring the displacement, we can determine the refractive index of the liquid. Beams of a He–Ne laser and a laser diode were used for measuring the refractive indices of pure water and some organic liquids.

© 1992 Optical Society of America

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References

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  1. B. W. Grange, W. H. Stevenson, R. Viskanta, “Refractive index of liquid solutions at low temperatures: an accurate measurement,” Appl. Opt. 15, 858–859 (1976).
    [CrossRef] [PubMed]
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    [CrossRef]
  3. W. Mahmood bin Mat Yunus, A. bin Abdul Rahman, “Refractive index of solutions at high concentrations,” Appl. Opt. 27, 3341–3343 (1988); Appl. Opt. 28, 2465(E) (1989).
    [CrossRef]
  4. K. Kuhler, E. L. Dereniak, M. Buchanan, “Measurement of the index of refraction of the plastic Phenoxy PKFE,” Appl. Opt. 30, 1711–1714 (1991).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. M. V. R. K. Murty, R. P. Shukla, “Simple method for measuring the refractive index of a liquid,” Opt. Eng. 18, 177–180 (1979).
  8. M. V. R. K. Murty, R. P. Shukla, “Liquid crystal wedge as a polarizing element and its use in shearing interferometry,” Opt. Eng. 19, 113–115 (1980).
  9. M. V. R. K. Murty, R. P. Shukla, “Simple method for measuring the refractive index of a liquid or glass wedge,” Opt. Eng. 22, 227–230 (1983).
  10. S. Nemoto, “Waist shift of a Gaussian beam by a dielectric plate,” Appl. Opt. 28, 1643–1647 (1989).
    [CrossRef] [PubMed]
  11. J.-C. Lee, S. D. Jacobs, “Refractive index and Δn/ΔT of Cr:Nd:GSGG at 1064 nm,” Appl. Opt. 26, 777–778 (1987).
    [CrossRef] [PubMed]
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    [CrossRef]
  13. H. R. Bilger, T. Habib, “Knife-edge scanning of an astigmatic Gaussian beam,” Appl. Opt. 24, 686–690 (1985).
    [CrossRef] [PubMed]

1991 (1)

1990 (1)

1989 (1)

1988 (1)

1987 (1)

1985 (1)

1984 (1)

1983 (1)

M. V. R. K. Murty, R. P. Shukla, “Simple method for measuring the refractive index of a liquid or glass wedge,” Opt. Eng. 22, 227–230 (1983).

1982 (1)

D. D. Jenkins, “Refractive indices of solutions,” Phys. Educ. 17, 82–83 (1982).
[CrossRef]

1980 (1)

M. V. R. K. Murty, R. P. Shukla, “Liquid crystal wedge as a polarizing element and its use in shearing interferometry,” Opt. Eng. 19, 113–115 (1980).

1979 (1)

M. V. R. K. Murty, R. P. Shukla, “Simple method for measuring the refractive index of a liquid,” Opt. Eng. 18, 177–180 (1979).

1976 (1)

1973 (1)

Bilger, H. R.

bin Abdul Rahman, A.

Buchanan, M.

de Greef, C.

Dereniak, E. L.

Dobbins, H. M.

Dushkina, N.

Finsy, R.

Grange, B. W.

Habib, T.

Jacobs, S. D.

Jenkins, D. D.

D. D. Jenkins, “Refractive indices of solutions,” Phys. Educ. 17, 82–83 (1982).
[CrossRef]

Kuhler, K.

Lee, J.-C.

Mahmood bin Mat Yunus, W.

Moreels, E.

Murty, M. V. R. K.

M. V. R. K. Murty, R. P. Shukla, “Simple method for measuring the refractive index of a liquid or glass wedge,” Opt. Eng. 22, 227–230 (1983).

M. V. R. K. Murty, R. P. Shukla, “Liquid crystal wedge as a polarizing element and its use in shearing interferometry,” Opt. Eng. 19, 113–115 (1980).

M. V. R. K. Murty, R. P. Shukla, “Simple method for measuring the refractive index of a liquid,” Opt. Eng. 18, 177–180 (1979).

Nemoto, S.

Peck, E. R.

Sainov, S.

Shukla, R. P.

M. V. R. K. Murty, R. P. Shukla, “Simple method for measuring the refractive index of a liquid or glass wedge,” Opt. Eng. 22, 227–230 (1983).

M. V. R. K. Murty, R. P. Shukla, “Liquid crystal wedge as a polarizing element and its use in shearing interferometry,” Opt. Eng. 19, 113–115 (1980).

M. V. R. K. Murty, R. P. Shukla, “Simple method for measuring the refractive index of a liquid,” Opt. Eng. 18, 177–180 (1979).

Stevenson, W. H.

Viskanta, R.

Appl. Opt. (8)

J. Opt. Soc. Am. (1)

Opt. Eng. (3)

M. V. R. K. Murty, R. P. Shukla, “Simple method for measuring the refractive index of a liquid,” Opt. Eng. 18, 177–180 (1979).

M. V. R. K. Murty, R. P. Shukla, “Liquid crystal wedge as a polarizing element and its use in shearing interferometry,” Opt. Eng. 19, 113–115 (1980).

M. V. R. K. Murty, R. P. Shukla, “Simple method for measuring the refractive index of a liquid or glass wedge,” Opt. Eng. 22, 227–230 (1983).

Phys. Educ. (1)

D. D. Jenkins, “Refractive indices of solutions,” Phys. Educ. 17, 82–83 (1982).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) Rectangular cell; (b) displacement of the beam axis that is due to the refraction by liquid and the cell walls.

Fig. 2
Fig. 2

Dependence of Δ/d2 on n2/n0 for various values of incident angle θ.

Fig. 3
Fig. 3

Dependence of Δ/d2 on incident angle θ for various values of n2/n0.

Fig. 4
Fig. 4

Experimental configuration that was used for measuring the beam displacement.

Fig. 5
Fig. 5

Variation of normalized photocurrent I/I0 with knife-edge position x for several values of incident angle θ. A 632.8-nm He–Ne laser beam was used. The solid curves were obtained from the least-squares method.

Fig. 6
Fig. 6

Variation of normalized photocurrent I/I0 with knife-edge position x for several values of incident angle θ. A beam emitted from a laser diode with 785-nm peak wavelength was used. The solid curves were obtained from the least-squares method.

Tables (2)

Tables Icon

Table 1 Measured Refractive Indices of Some Liquids at 632.8 nm

Tables Icon

Table 2 Measured Refractive Indices of Some Liquids at 785 nm and Those Calculated from a Single-Term Sellmeier Equation

Equations (23)

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δ i = d i / ( sin θ + cos θ / tan ϕ i ) ,
ϕ i = θ - sin - 1 [ ( n 0 / n i ) sin θ ] ,             i = 1 , 2 ,
δ i = d i [ 1 - n 0 cos θ / ( n i 2 - n 0 2 sin 2 θ ) 1 / 2 ] sin θ .
δ ( n 0 , n 1 , n 2 ) = { 2 d 1 [ 1 - n 0 cos θ / ( n 1 2 - n 0 2 sin 2 θ ) 1 / 2 ] + d 2 [ 1 - n 0 cos θ / ( n 2 2 - n 0 2 sin 2 θ ) 1 / 2 ] } sin θ .
Δ δ ( n 0 , n 1 , n 2 ) - δ ( n 0 , n 1 , n 0 ) .
Δ = d 2 [ 1 - n 0 cos θ / ( n 2 2 - n 0 2 sin 2 θ ) 1 / 2 ] sin θ ,
n 2 = n 0 { 1 + [ cos θ / ( sin θ - Δ / d 2 ) ] 2 } 1 / 2 sin θ .
( Δ / d 2 ) / ( n 2 / n 0 ) = ( n 2 / n 0 ) sin θ cos θ / [ ( n 2 / n 0 ) 2 - sin 2 θ ] 3 / 2 ,
n w = 1.332156 - [ 8.889 ( t - 20 ) + 0.1610 ( t - 20 ) 2 ] × 10 - 5 ,
n w = 1.1457 + 0.1365 × 10 - 2 T - 0.2486 × 10 - 5 T 2 ,
n w 2 = 1 + 0.75260 λ 2 / ( λ 2 - 10212.8 ) ,
n e 2 = 1 + 0.82998 λ 2 / ( λ 2 - 9740.5 ) ,
n 2 / Δ = ( n 0 / d 2 ) sin θ cos 2 θ ( sin θ - Δ / d 2 ) - 2 × [ ( sin θ - Δ / d 2 ) 2 + cos 2 θ ] - 1 / 2 ,
n 2 / θ = - ( Δ / d 2 ) [ 1 - ( Δ / d 2 ) sin θ + ( sin θ - Δ / d 2 ) 2 ] cos θ × ( sin θ - Δ / d 2 ) - 2 × [ ( sin θ - Δ / d 2 ) 2 + cos 2 θ ] - 1 / 2 ,
tan ϕ i = ( sin θ cos θ i - cos θ sin θ i ) ( cos θ cos θ i + sin θ sin θ i ) .
sin θ i = ( n 0 / n i ) sin θ , cos θ i = [ 1 - ( n 0 / n i ) 2 sin 2 θ ] 1 / 2
tan ϕ i = [ ( n c - n 0 cos θ ) / ( n c cos θ + n 0 sin 2 θ ) ] sin θ ,
sin θ + cos θ / tan ϕ i = n c / [ ( n c - n 0 cos θ ) sin θ ] .
p = ( P 0 / π s 2 ) exp { - [ ( x - x 0 ) 2 + ( y - y 0 ) 2 ] / s 2 } ,
P = - x 1 - p d x d y = [ P 0 / ( 2 π ) ] - u exp ( - t 2 / 2 ) d t ,
Q ( u ) [ 1 / ( 2 π ) ] u exp ( - t 2 / 2 ) d t ,
Q ( u ) = 1 / { 1 + exp [ f ( u ) ] } ,
f ( u ) = 1.595700 u + 0.072953 u 3 - 0.000324 u 5 - 0.0000350 u 7 .

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