Abstract

When a transparent plane-parallel plate is illuminated at a boundary region by a monochromatic parallel beam of light, Fresnel diffraction occurs because of the abrupt change in phase imposed by the finite change in refractive index at the plate boundary. The visibility of the diffraction fringes varies periodically with changes in incident angle. The visibility period depends on the plate thickness and the refractive indices of the plate and the surrounding medium. Plotting the phase change versus incident angle or counting the visibility repetition in an incident-angle interval provides, for a given plate thickness, the refractive index of the plate very accurately. It is shown here that the refractive index of a plate can be determined without knowing the plate thickness. Therefore, the technique can be utilized for measuring plate thickness with high precision. In addition, by installing a plate with known refractive index in a rectangular cell filled with a liquid and following the described procedures, the refractive index of the liquid is obtained. The technique is applied to measure the refractive indices of a glass slide, distilled water, and ethanol. The potential and merits of the technique are also discussed.

© 2012 Optical Society of America

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References

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2010 (2)

2009 (2)

2008 (1)

2007 (2)

2005 (1)

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, Opt. Commun. 255, 23 (2005).
[CrossRef]

2000 (2)

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, Opt. Commun. 175, 315 (2000).
[CrossRef]

M. A. Khashan and A. Y. Nassif, Appl. Opt. 39, 5991 (2000).
[CrossRef]

1982 (1)

Alipour, R.

Alirezaei, Z.

Amiri, M.

Beaumont, A.

Darudi, A.

de Angelis, M.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, Opt. Commun. 175, 315 (2000).
[CrossRef]

De Nicola, S.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, Opt. Commun. 175, 315 (2000).
[CrossRef]

Dolatkhah, H.

Ferraro, P.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, Opt. Commun. 175, 315 (2000).
[CrossRef]

Finizio, A.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, Opt. Commun. 175, 315 (2000).
[CrossRef]

Haghighi, I. M.

Hart, C.

Hassani, K.

Kafri, O.

Kao, C.-F.

Karimi, E.

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, Opt. Commun. 255, 23 (2005).
[CrossRef]

Karmy, Z.

Khalesifard, H. R.

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, Opt. Commun. 255, 23 (2005).
[CrossRef]

Khashan, M. A.

Liu, T.-S.

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics, 3rd ed. (Longman, 1973), pp. 93–95.

Lu, S-H.

Moradi, A. R.

Nassif, A. Y.

Pan, S.-P.

Pierattini, G.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, Opt. Commun. 175, 315 (2000).
[CrossRef]

Saber, A.

Tavassoly, M. T.

Tedaldi, M.

Tomlins, P. H.

Wooliams, P.

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of Fresnel diffraction from a phase plate. The abrupt change in refractive index at the boundary of a transparent plate, NN, results in diffraction fringes on a screen perpendicular to the light-propagation direction.

Fig. 2.
Fig. 2.

Diffraction patterns and corresponding intensity distributions obtained by the diffraction of p-polarized light from the edge of a plane-parallel plate of thickness 0.9996 mm in transmission mode at incident angles close to Brewster’s angle. The corresponding phases are (a) mπ, (b) (m+4/9)π, (c) (m+6/9)π, (d) (m+10/9)π, (e) (m+14/9)π, and (f) (m+2)π, where m is an odd number.

Fig. 3.
Fig. 3.

Sketch of the experimental setup. The labels LB, BE, S, CCD, and PC respectively denote the laser beam, beam expander, sample, detector, and personal computer.

Fig. 4.
Fig. 4.

Experimental phase change versus incident angle (points) obtained by diffraction of light from the edge of a glass slide immersed in air (a) and distilled water (b). The solid curves are the corresponding theoretical fits.

Tables (1)

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Table 1. Refractive Indices Obtained Using Fresnel Diffraction from a Phase Plate

Equations (3)

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φ=2πhλN(n2sin2θcosθ),
V=12(IL,max+IR,max)IC,min12(IL,max+IR,max)+IC,min,
φ=2πhλ(N2sin2θN2sin2θ),

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