Quantitative investigation of Fresnel reflection in the electromagnetism laboratory

American Journal of Physics

Volumn 67, Issue 7, 1999, Pages 605-612

  Dekker, M ^a   Kromminga, A J ^a   Van Baak, D A ^a   Pilskalns, O J ^b   Jacobs, J P ^b  

^a CALVIN COLLEGE   (United States)

^b UNIVERSITY OF MONTANA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039440841     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.19331     Document Type: Article

References (24)

1. For example, see P. Lorrain and D. R. Corson, Electromagnetic Fields and Waves (Freeman, San Francisco, 1970), 2nd ed., pp. 508-519 or D. J. Griffiths, Introduction to Electrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1989), 2nd ed., pp. 363-368.
2. For example, see P. Lorrain and D. R. Corson, Electromagnetic Fields and Waves (Freeman, San Francisco, 1970), 2nd ed., pp. 508-519 or D. J. Griffiths, Introduction to Electrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1989), 2nd ed., pp. 363-368.
3. Edward Collett, "Mueller-Stokes matrix formulation of Fresnel's equations," Am. J. Phys. 39, 517-528 (1971); William T. Doyle, "Graphical approach to Fresnel's equations for reflection and refraction of light," ibid. 48, 643-647 (1980); R. K. P. Zia, "Symmetric Fresnel equations: An energy conservation approach," ibid. 56, 555-558 (1988).
4. Edward Collett, "Mueller-Stokes matrix formulation of Fresnel's equations," Am. J. Phys. 39, 517-528 (1971); William T. Doyle, "Graphical approach to Fresnel's equations for reflection and refraction of light," ibid. 48, 643-647 (1980); R. K. P. Zia, "Symmetric Fresnel equations: An energy conservation approach," ibid. 56, 555-558 (1988).
5. Edward Collett, "Mueller-Stokes matrix formulation of Fresnel's equations," Am. J. Phys. 39, 517-528 (1971); William T. Doyle, "Graphical approach to Fresnel's equations for reflection and refraction of light," ibid. 48, 643-647 (1980); R. K. P. Zia, "Symmetric Fresnel equations: An energy conservation approach," ibid. 56, 555-558 (1988).
6. H. S. T. Driver, "An undergraduate experiment to measure the reflectances of a dielectric surface," Am. J. Phys. 46, 696-699 (1978).
7. D. Brewster, "On the laws which regulate the polarization of light by reflexion from transparent bodies," Philos. Trans. R. Soc. London 105, 125-159 (1815).
8. A. J. Fresnel, "[Extrait d'un Mémoire] sur la loi des modifications imprimées à la lumière polarisé par sa réflexion totale dans l'intérieur des corps transparents," Ann. Chim. (Paris) 29, 175-87 (1825). Also in Oeuvres Complètes D'Augustin Fresnel (Imprimérie Impériale, Paris, 1866-1870), Vol. 1, pp. 753-762.
9. A. J. Fresnel, "[Extrait d'un Mémoire] sur la loi des modifications imprimées à la lumière polarisé par sa réflexion totale dans l'intérieur des corps transparents," Ann. Chim. (Paris) 29, 175-87 (1825). Also in Oeuvres Complètes D'Augustin Fresnel (Imprimérie Impériale, Paris, 1866-1870), Vol. 1, pp. 753-762.
10. A survey of this history appears in E. T. Whittaker, A History of the Theories of Æther & Electricity (Dover, New York, 1989), Chap. IV.
11. The equations were verified at normal incidence by Arago in the visible and by Provostaye and Desains in the IR (Ref. 8, p. 363). In Ref. 9 on p. 392, Buchwald states: "[The Fresnel equations]... could not in any case be tested themselves, since accurate photometric techniques were not available... ." Certain implications of the equations were tested, however, and by 1830 they were generally accepted as empirical rules without a proper theoretical basis (Ref. 9).
12. Thomas Preston, The Theory of Light (Macmillan, London, 1912), 4th ed.
13. Jed Z. Buchwald, The Rise of the Wave Theory of Light (The University of Chicago Press, Chicago, 1989).
14. The derivation was first performed explicitly by H. A. Lorentz in 1875 (see Ref. 9, p. 392).
15. IR viewing cards can be purchased for only a few dollars at many electronics vendors including Radio Shack.
16. For the 670-nm experiment we used commercial diode-laser modules, consisting of diode-laser package, collimating lens, and power-conditioning board (Beta Electronics M2670, though DigiKey 11043-ND might be more accessible). For the 780-nm experiment we used a Sharp 5-mW (LT022MD) laser driven with an APC circuit module made by Thor Labs (LD1100). The laser is mounted in a 9-mm type collimating tube with collimating lens (similar to Thor Labs LT110P). The main desiderata of both systems are APC and an adjustable focusing lens.
17. In the 670-nm system we achieve this alignment by rotating the module within the block at such an angle as to minimize the optical power reflected at an interface encountered near Brewster's angle. Alternatively, as in the 780-nm system, one can mount the collimating tube in a rotation stage (Thor Labs RSP1) which allows for precise rotation of the entire laser head to adjust the plane of polarization of the incident light. The rotation stage is in turn mounted on a two-axis mirror mount (Thor Lab KM1) to allow for precise steering of the laser beam. More advanced experiments can be performed with the laser set to arbitrary polarization angle, in which case the reflected intensity can be predicted by proper combination of Eqs. (1) and (2).
18. 2 active area. For the smaller active area diodes we use an iris diaphragm (Thor Labs ID12) after the laser to reduce the beam size so that it fits on the detector.
19. A current of 1 mA from a photodiode will create a 100-mV potential difference across such a meter, and the photodiode; but because of the shape of the current-voltage curve for an illuminated photodiode, this creates an error of order 1 μA or less in the measured current. Alternatively, one can connect the photodiode to an op-amp current-to-voltage converter and measure the output with a voltmeter. This removes any current errors of the type described above, since the photodiode anode is at virtual ground. This method is used in the 780-nm experiment.
20. The largest systematic error is not drift in the optical power received, but point-to-point variations in the photodiode sensitivity. Purpose-crafted photodiodes (unlike solar cells) keep such sensitivity variations under 1%, but it is still worthwhile to keep the laser beam aimed at the center of the photodiode.
21. This is preferred to turning the laser on and off electrically, since blocking the beam does not disturb the temperature equilibration of the laser power.
22. David H. Sliney et al., "Visual sensitivity of the eye to infrared laser radiation," J. Opt. Soc. Am. 66, 339-341 (1976).
23. Laser Safety Guide (Laser Institute of America, 1991) presentation of the Z136.1 guidelines for maximum permissible exposure for direct ocular exposure.
24. P. R. Bevington, Data Reduction and Error Analysis in the Physical Sciences (McGraw-Hill, New York, 1969).