Abstract

Measurements of lens parameters such as focal length, radius of curvature, and refractive index are important. We describe a measurement method that utilizes a Michelson interferometer to determine parameters of thin, convex lenses. The real fringe system formed by a Michelson interferometer is used to determine the focal lengths and the radii of curvature of the lenses. The refractive index of the lens material is determined from the thin-lens formula. We were able to determine the refractive indices to an accuracy as great as 99.97%. A detailed theoretical and experimental analysis is given.

© 2006 Optical Society of America

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References

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  1. E. Hecht, Optics (Addison-Wesley, 1998).
  2. G. Smith, "Liquid immersion method for the measurement of the refractive index of a lens," Appl. Opt. 21, 755-758 (1982).
    [CrossRef] [PubMed]
  3. R. S. Kasana and K. J. Rosenbrunch, "Determination of the refractive index of a lens using the Murty shearing interferometer," Appl. Opt. 22, 3526-3531 (1983).
    [CrossRef] [PubMed]
  4. R. S. Kasana and K. J. Rosenbrunch, "The use of a plane parallel plate for determining the lens' parameters," Opt. Commun. 46, 69-73 (1983).
    [CrossRef]
  5. R. P. Shukla, G. M. Perera, M. C. George, and P. Venkateswaralu, "Determination of refractive index of a simple negative, positive, or zero power lens using wedged plate interferometer," Appl. Opt. 29, 4541-4543 (1990).
    [CrossRef] [PubMed]
  6. R. P. Shukla and D. Malacara, "Some applications of the Murty interferometer: a review," Opt. Lasers Eng. 26, 1-42 (1997).
    [CrossRef]
  7. R. S. Kasana, S. Boseck, and K. J. Rosenbrunch, "Use of a grating in a coherent optical-processing configuration for evaluting the refractive index of a lens," Appl. Opt. 23, 757-761 (1984).
    [CrossRef] [PubMed]
  8. C. S. Narayanamurthy, "Collimation testing using temporal coherence," Opt. Eng. 35, 1161-1164 (1996).
    [CrossRef]
  9. Melles Griot, The Practical Application of Light, Melles Griot Catalogue for Optical Components, http://www.mellesgriot.com (2000).

1997 (1)

R. P. Shukla and D. Malacara, "Some applications of the Murty interferometer: a review," Opt. Lasers Eng. 26, 1-42 (1997).
[CrossRef]

1996 (1)

C. S. Narayanamurthy, "Collimation testing using temporal coherence," Opt. Eng. 35, 1161-1164 (1996).
[CrossRef]

1990 (1)

1984 (1)

1983 (2)

R. S. Kasana and K. J. Rosenbrunch, "The use of a plane parallel plate for determining the lens' parameters," Opt. Commun. 46, 69-73 (1983).
[CrossRef]

R. S. Kasana and K. J. Rosenbrunch, "Determination of the refractive index of a lens using the Murty shearing interferometer," Appl. Opt. 22, 3526-3531 (1983).
[CrossRef] [PubMed]

1982 (1)

Boseck, S.

George, M. C.

Griot, Melles

Melles Griot, The Practical Application of Light, Melles Griot Catalogue for Optical Components, http://www.mellesgriot.com (2000).

Hecht, E.

E. Hecht, Optics (Addison-Wesley, 1998).

Kasana, R. S.

Malacara, D.

R. P. Shukla and D. Malacara, "Some applications of the Murty interferometer: a review," Opt. Lasers Eng. 26, 1-42 (1997).
[CrossRef]

Narayanamurthy, C. S.

C. S. Narayanamurthy, "Collimation testing using temporal coherence," Opt. Eng. 35, 1161-1164 (1996).
[CrossRef]

Perera, G. M.

Rosenbrunch, K. J.

Shukla, R. P.

Smith, G.

Venkateswaralu, P.

Appl. Opt. (4)

Opt. Commun. (1)

R. S. Kasana and K. J. Rosenbrunch, "The use of a plane parallel plate for determining the lens' parameters," Opt. Commun. 46, 69-73 (1983).
[CrossRef]

Opt. Eng. (1)

C. S. Narayanamurthy, "Collimation testing using temporal coherence," Opt. Eng. 35, 1161-1164 (1996).
[CrossRef]

Opt. Lasers Eng. (1)

R. P. Shukla and D. Malacara, "Some applications of the Murty interferometer: a review," Opt. Lasers Eng. 26, 1-42 (1997).
[CrossRef]

Other (2)

Melles Griot, The Practical Application of Light, Melles Griot Catalogue for Optical Components, http://www.mellesgriot.com (2000).

E. Hecht, Optics (Addison-Wesley, 1998).

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Figures (6)

Fig. 1
Fig. 1

Setup for finding the focal length of a convex lens.

Fig. 2
Fig. 2

Michelson interferometer with (a) a diverging wavefront with l 2l 1 = d ≠ 0, (b) a diverging wavefront illumination with l 2l 1 = d = 0, (c) a collimated wavefront with l 2l 1 = d ≠ 0.

Fig. 3
Fig. 3

Setup for finding the radius of curvature of a lens.

Fig. 4
Fig. 4

Change in interference pattern with lens position x for a 200 mm focal-length lens with λ = 632.8 nm: (a) x = 198 mm, (b) x = at focus, (c) x = 202 mm.

Fig. 5
Fig. 5

Change in interference pattern with lens position from focusing lens y for a 200 mm focal-length lens: (a) y = 281 mm, (b) y = y 1 = 293.39 mm, (c) y = 304 mm, (d) y = y 2 = 500 mm. Radius of curvature, R = y 2y 1 = 206.61 mm.

Fig. 6
Fig. 6

Change in refractive index with wavelength for lenses of various focal lengths: (a) f = 200 mm, (b) f = 300 mm, (c) f = 400 mm. The error bar shown is 0.03% of the experimental data.

Tables (3)

Tables Icon

Table 1 Focal Length and Error Measured with a 632.8 nm Laser

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Table 2 Measured Radii of Curvature and Errors in Measurement

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Table 3 Comparison of Measured and Literature Values of Refractive Index

Equations (6)

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Δ x = R 1 R 2 = 2 d cos ( θ ) ,
d = l 2 l 1
R = y 2 y 1 .
n = 1 + R 1 R 2 f ( R 2 R 1 ) ,
d n = ± ( d R 2 f R 2 f 2 d f ) .
d n = ± [ d R 2 f ( n 1 ) 2 f d f ] .

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