Abstract

A very simple method to obtain the refractive index of liquids by using a rectangular glass cell and a diffraction grating engraved by fs laser ablation on the inner face of one of the walls of the cell is presented. When a laser beam impinges normally on the diffraction grating, the diffraction orders are deviated when they pass through the cell filled with the liquid to be measured. By measuring the deviation of the diffraction orders, we can determine the refractive index of the liquid.

© 2014 Optical Society of America

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References

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  1. M. De Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A reflective grating interferometer for measuring the refractive index of liquids,” Pure Appl. Opt. 5(6), 761–765 (1996).
    [Crossref]
  2. S. Singh, “Diffraction method measures refractive indices of liquids,” Phys. Educ. 39(3), 235 (2004).
    [Crossref]
  3. J. Warren, Smith, “Diffraction grating,” in Modern Optical Engineering, ed. (McGraw-Hill SPIE, 2000).
  4. S. Kedemburg, M. Vieweg, T. Gissibl, A. Finizio, and H. Giessen, “Linear refractive index and absorption measurement of nonlinear optical liquids in the visible and near-infrared spectral region,” Opt. Mater. Express 2, 1588–1611 (2011).
  5. S. Ariponnammal, “A novel method of using refractive index as a tool for finding the adultration of oils,” Res. J. Recent Sci. 17, 77–79 (2012).

2012 (1)

S. Ariponnammal, “A novel method of using refractive index as a tool for finding the adultration of oils,” Res. J. Recent Sci. 17, 77–79 (2012).

2011 (1)

2004 (1)

S. Singh, “Diffraction method measures refractive indices of liquids,” Phys. Educ. 39(3), 235 (2004).
[Crossref]

1996 (1)

M. De Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A reflective grating interferometer for measuring the refractive index of liquids,” Pure Appl. Opt. 5(6), 761–765 (1996).
[Crossref]

Ariponnammal, S.

S. Ariponnammal, “A novel method of using refractive index as a tool for finding the adultration of oils,” Res. J. Recent Sci. 17, 77–79 (2012).

De Angelis, M.

M. De Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A reflective grating interferometer for measuring the refractive index of liquids,” Pure Appl. Opt. 5(6), 761–765 (1996).
[Crossref]

De Nicola, S.

M. De Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A reflective grating interferometer for measuring the refractive index of liquids,” Pure Appl. Opt. 5(6), 761–765 (1996).
[Crossref]

Ferraro, P.

M. De Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A reflective grating interferometer for measuring the refractive index of liquids,” Pure Appl. Opt. 5(6), 761–765 (1996).
[Crossref]

Finizio, A.

S. Kedemburg, M. Vieweg, T. Gissibl, A. Finizio, and H. Giessen, “Linear refractive index and absorption measurement of nonlinear optical liquids in the visible and near-infrared spectral region,” Opt. Mater. Express 2, 1588–1611 (2011).

M. De Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A reflective grating interferometer for measuring the refractive index of liquids,” Pure Appl. Opt. 5(6), 761–765 (1996).
[Crossref]

Giessen, H.

Gissibl, T.

Kedemburg, S.

Pierattini, G.

M. De Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A reflective grating interferometer for measuring the refractive index of liquids,” Pure Appl. Opt. 5(6), 761–765 (1996).
[Crossref]

Singh, S.

S. Singh, “Diffraction method measures refractive indices of liquids,” Phys. Educ. 39(3), 235 (2004).
[Crossref]

Vieweg, M.

Opt. Mater. Express (1)

Phys. Educ. (1)

S. Singh, “Diffraction method measures refractive indices of liquids,” Phys. Educ. 39(3), 235 (2004).
[Crossref]

Pure Appl. Opt. (1)

M. De Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A reflective grating interferometer for measuring the refractive index of liquids,” Pure Appl. Opt. 5(6), 761–765 (1996).
[Crossref]

Res. J. Recent Sci. (1)

S. Ariponnammal, “A novel method of using refractive index as a tool for finding the adultration of oils,” Res. J. Recent Sci. 17, 77–79 (2012).

Other (1)

J. Warren, Smith, “Diffraction grating,” in Modern Optical Engineering, ed. (McGraw-Hill SPIE, 2000).

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Figures (6)

Fig. 1
Fig. 1 Diffractometer used for measuring the refractive index of liquid substances.
Fig. 2
Fig. 2 Diffraction angles and paths for the m order beam in the two cases: when the cell is empty and when the cell is filled with the liquid.
Fig. 3
Fig. 3 Experimental arrangement used to obtain the refractive index of liquids.
Fig. 4
Fig. 4 Optical scheme used to detect the positions of the spots of the diffraction orders.
Fig. 5
Fig. 5 Diffraction grating of 6 μm engraved on the inner face of one wall of the cell.
Fig. 6
Fig. 6 Images of the spots of first-order for: (a) air and (b) water.

Tables (1)

Tables Icon

Table1 Measured refractive indices n2 of the water, castor oil and alcohol at 532 nm.

Equations (18)

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sin θ m = mλ S ±sinI,
λ= λ 0 n .
sin θ m = m λ 0 nS ±sinI.
sin θ m = m λ 0 nS +sinI.
( d i ) m =wtan ( θ i ) m =w sin ( θ i ) m 1 sin 2 ( θ i ) m ,
sin ( θ i ) m = m λ 0 n i S +sinI,     i= 1, 2  and  m= 1, 2, 3,,
Δ d m = ( d 1 ) m ( d 2 ) m ,   m= 1, 2, 3,,  
Δ d m =w m λ 0 S ( 1 1 ( m λ 0 S +sinI ) 2 1 n 2 2 ( m λ 0 S + n 2 sinI ) 2 ).
n 2 = m λ 0 S ( 1+ ( Δ d m /w m λ 0 /S +sinI 1 ( m λ 0 /S +sinI ) 2 ) 2 Δ d m /w m λ 0 /S +sinI 1 ( m λ 0 /S +sinI ) 2 +sinI 1+ ( Δ d m /w m λ 0 /S +sinI 1 ( m λ 0 /S +sinI ) 2 ) 2 ),
sin ( θ i ) m = m λ 0 n i S ,    i= 1,2  and  m= 1, 2, 3,,
n 2 = m λ 0 S 1+ w 2 ( 1 m 2 λ 0 2 S 2 ) ( w m λ 0 S Δ d m 1 m 2 λ 0 2 S 2 ) 2 .
n 1 sin ( θ 1 ) m =nsin ( α 1 ) m ,
n 2 sin ( θ 2 ) m =nsin ( α 2 ) m ,
Δ d m = ( D 1 ) m ( D 2 ) m .
n 2 / Δ d m = ( w 2 m λ 0 /S ) ( 1 m 2 λ 0 2 / S 2 ) 3 ( w m λ 0 /S Δ d m 1 m 2 λ 0 2 / S 2 ) 3 1+ w 2 ( 1 m 2 λ 0 2 / S 2 ) / ( w m λ 0 /S Δ d m 1 m 2 λ 0 2 /S 2 ) 2 .
n 2 / I = A m ( m λ 0 cosI ) B m 2 ( 2 S 2 P m Q m ) .
A m =2 w 2 S 3 + Q m { 2wΔ d m [ m λ 0 ( S 2 +2 m 2 λ 0 2 3 S 2 cos2I )SsinI( S 2 6 m 2 λ 0 2 + S 2 cos2I ) ] +S P m [ S 2 ( 2 w 2 + ( Δ d m ) 2 )2 m 2 ( Δ d m ) 2 λ 0 2 +S ( Δ d m ) 2 ( Scos2I4m λ 0 sinI ) ] }, B m =w( m λ 0 +SsinI )S P m ( Δ d m +wQ s m inI ), P m = 1 ( m λ 0 /S +sinI ) 2 ,
Q m = 1+ [ Δ d m /w ( m λ 0 /S +sinI ) / 1 ( m λ 0 /S +sinI ) 2 ] 2 .

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