Abstract

This paper concerns tables of Fresnel intensity reflectances which resulted from studies based on classical electrodynamics. The tables contain approximately 2500 indices of refraction <i>N</i> = <i>n</i> - <i>ki</i>; i.e., <i>n</i> = 0.1 (0.1) 4.0, <i>k</i> = 0(0.1) 6.0 for angles of incidence θ<sub>0</sub> = 0° (5°) 85°. Series of graphs illustrate the solutions of the Fresnel equations. The supplementary discussion describes in detail the occurrence of reflection characteristics for which (a) the amplitude of the wave oscillating parallel to the plane of incidence is a minimum, (b) the degree of polarization is a maximum, and (c) the two amplitudes of the reflected wave have a 90° difference of phase. The numerical solutions are also presented in graphs that provide means, in addition to those already in general use, of determining the indices of refraction of solid materials.

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  1. Herbert B. Holl, "The Effect of Radiation Force on Satellites of Convex Shape," NASA TN D-604 (May 1961).
  2. Herbert B. Holl, "The Reflection of Electromagnetic Radiation (Based on Classical Electrodynamics)," Vol. I (AD422882), Vol. II (AD600720), "Appendix-Tables of Radiation Reflection Functions," U. S. Army Missile Command, Redstone Arsenal, Alabama, Report No. RF-TR-63-4 (15 March 1963).
  3. W. König, "Elektromagnetische Lichttheorie," in Handbuch der Physik (Springer, Berlin, 1928), Vol. XX.
  4. R. Minkowski, "Theorie der Reflexion, Brechung und Dispersion," in Müller-Pouillet's Lehrbuch der Physik (Friedr. Vieweg und Sohn Akt. Ges., Braunschweig, 1929).
  5. Julius A. Stratton, Electromagnetic Theory (McGraw-Hill Book Company, Inc., New York, 1941).
  6. Max Born and Emil Wolf, Principles of Optics (Pergamon Press, New York, 1959).
  7. Richard Tousey, J. Opt. Soc. Am. 29, 235 (1939).
  8. Parry Moon, J. Math. Phys. 19, 1 (1940).
  9. Ivan Šimon, J. Opt. Soc. Am. 41, 336 (1951).
  10. D. G. Avery, Proc. Phys. Soc. (London) 65, 425 (1952).
  11. Gerhard Heilmann, Physik 152, 368 (1958).
  12. Kozo Ishiguro, Taizo Sasaki, and Sadao Nomura, Sci. Papers of the College of General Education, University of Tokyo 10, 207 (1960).
  13. S. P. F. Humphreys-Owen, Proc. Phys. Soc. (London) 77, 949 (1961).
  14. H. G. Häfele, Physik 168, 530 (1962).
  15. A. P. Prishivalko, Reflection of Light from Absorbing Media (Academy of Sciences of White Russian SSR, Minsk, 1963).
  16. Antonín Vašiček, Tables of Determination of Optical Constants from the Intensities of Reflected Light (Nakladatelství Ceskoslovenskí Akademie VĚD, Praha, 1964).
  17. The information about Dr. A. P. Prishivalko's work was furnished by Professor Dr. Antonín Vašiček, University Brno, Czeckoslavakia, who also supplied a copy of the former's book which contained the tables. The author is deeply indebted to Dr. Vašíček for these kindnesses.
  18. Background details and complete sequence of equations on which this discussion is based can be found in Ref. 2.
  19. Expressions for the first and second Brewster angles can be obtained by differentiation of expressions based on Eqs. (2) and (3). To do this, however, requires tedious analytical labor, and it has previously been considered impossible to solve this problem explicitly (Refs. 20, 21) so that only approximations were sought. The problem found new consideration recently, and was explicitly solved for the first Brewster angle by Humphreys-Owen13 and for the second Brewster angle by Potter.22
  20. C. Boeckner, J. Opt. Soc. Am. and Rev. Sci. Instr. 19, 7 (1929).
  21. P. H. Miller, Jr., and J. R. Johnson, Physica 20, 11, 1026 (1954).
  22. Roy F. Potter, J. Opt. Soc. Am. 54, 904 (1964).
  23. These tables were for internal use only and were not published in Holl.2
  24. Paul Drude, The Theory of Optics (Dover Publications, Inc., New York, 1959).
  25. A similar equation given by König3 [Eq. (169b), p. 246] is found to be incorrect.
  26. Herbert B. Holl, Numerical Solutions of the Fresnel Equations in the Optical Region, Symposium on Thermal Radiation of Solids, NASA SP-55, AF ML-TDR-64-159 (National Aeronautics & Space Administration, Washington, D. C, 1965), p. 45.
  27. R. W. Wood, Phys. Rev. 44, 353 (1933).
  28. R. de L. Kronig [Nature, Feb. 10, 211 (1934)] obtained, for potassium, N = 0.294–0.0058i for λ = 2727 Å.
  29. Felix Jentzsch-Gräfe [Verhandl. Deut. Phys. Ges. 21, 361, (1919)] thoroughly investigated the minimum reflectance of natural light for real index of refraction. His paper presented an exact mathematical formulation for this case and tabulated the values for θ0 and R=min from n=3.7321 to n=9.507.

Avery, D. G.

D. G. Avery, Proc. Phys. Soc. (London) 65, 425 (1952).

Boeckner, C.

C. Boeckner, J. Opt. Soc. Am. and Rev. Sci. Instr. 19, 7 (1929).

Born, Max

Max Born and Emil Wolf, Principles of Optics (Pergamon Press, New York, 1959).

Drude, Paul

Paul Drude, The Theory of Optics (Dover Publications, Inc., New York, 1959).

Häfele, H. G.

H. G. Häfele, Physik 168, 530 (1962).

Heilmann, Gerhard

Gerhard Heilmann, Physik 152, 368 (1958).

Holl, Herbert B.

Herbert B. Holl, "The Effect of Radiation Force on Satellites of Convex Shape," NASA TN D-604 (May 1961).

Herbert B. Holl, "The Reflection of Electromagnetic Radiation (Based on Classical Electrodynamics)," Vol. I (AD422882), Vol. II (AD600720), "Appendix-Tables of Radiation Reflection Functions," U. S. Army Missile Command, Redstone Arsenal, Alabama, Report No. RF-TR-63-4 (15 March 1963).

Herbert B. Holl, Numerical Solutions of the Fresnel Equations in the Optical Region, Symposium on Thermal Radiation of Solids, NASA SP-55, AF ML-TDR-64-159 (National Aeronautics & Space Administration, Washington, D. C, 1965), p. 45.

Humphreys-Owen, S. P. F.

S. P. F. Humphreys-Owen, Proc. Phys. Soc. (London) 77, 949 (1961).

Ishiguro, Kozo

Kozo Ishiguro, Taizo Sasaki, and Sadao Nomura, Sci. Papers of the College of General Education, University of Tokyo 10, 207 (1960).

Jentzsch-Gräfe, Felix

Felix Jentzsch-Gräfe [Verhandl. Deut. Phys. Ges. 21, 361, (1919)] thoroughly investigated the minimum reflectance of natural light for real index of refraction. His paper presented an exact mathematical formulation for this case and tabulated the values for θ0 and R=min from n=3.7321 to n=9.507.

Johnson, J. R.

P. H. Miller, Jr., and J. R. Johnson, Physica 20, 11, 1026 (1954).

König, W.

W. König, "Elektromagnetische Lichttheorie," in Handbuch der Physik (Springer, Berlin, 1928), Vol. XX.

Kronig, R. de L.

R. de L. Kronig [Nature, Feb. 10, 211 (1934)] obtained, for potassium, N = 0.294–0.0058i for λ = 2727 Å.

Miller, Jr., P. H.

P. H. Miller, Jr., and J. R. Johnson, Physica 20, 11, 1026 (1954).

Minkowski, R.

R. Minkowski, "Theorie der Reflexion, Brechung und Dispersion," in Müller-Pouillet's Lehrbuch der Physik (Friedr. Vieweg und Sohn Akt. Ges., Braunschweig, 1929).

Moon, Parry

Parry Moon, J. Math. Phys. 19, 1 (1940).

Nomura, Sadao

Kozo Ishiguro, Taizo Sasaki, and Sadao Nomura, Sci. Papers of the College of General Education, University of Tokyo 10, 207 (1960).

Potter, Roy F.

Roy F. Potter, J. Opt. Soc. Am. 54, 904 (1964).

Prishivalko, A. P.

A. P. Prishivalko, Reflection of Light from Absorbing Media (Academy of Sciences of White Russian SSR, Minsk, 1963).

Sasaki, Taizo

Kozo Ishiguro, Taizo Sasaki, and Sadao Nomura, Sci. Papers of the College of General Education, University of Tokyo 10, 207 (1960).

Šimon, Ivan

Ivan Šimon, J. Opt. Soc. Am. 41, 336 (1951).

Stratton, Julius A.

Julius A. Stratton, Electromagnetic Theory (McGraw-Hill Book Company, Inc., New York, 1941).

Tousey, Richard

Richard Tousey, J. Opt. Soc. Am. 29, 235 (1939).

Vašicek, Antonín

Antonín Vašiček, Tables of Determination of Optical Constants from the Intensities of Reflected Light (Nakladatelství Ceskoslovenskí Akademie VĚD, Praha, 1964).

The information about Dr. A. P. Prishivalko's work was furnished by Professor Dr. Antonín Vašiček, University Brno, Czeckoslavakia, who also supplied a copy of the former's book which contained the tables. The author is deeply indebted to Dr. Vašíček for these kindnesses.

Wolf, Emil

Max Born and Emil Wolf, Principles of Optics (Pergamon Press, New York, 1959).

Wood, R. W.

R. W. Wood, Phys. Rev. 44, 353 (1933).

Other (29)

Herbert B. Holl, "The Effect of Radiation Force on Satellites of Convex Shape," NASA TN D-604 (May 1961).

Herbert B. Holl, "The Reflection of Electromagnetic Radiation (Based on Classical Electrodynamics)," Vol. I (AD422882), Vol. II (AD600720), "Appendix-Tables of Radiation Reflection Functions," U. S. Army Missile Command, Redstone Arsenal, Alabama, Report No. RF-TR-63-4 (15 March 1963).

W. König, "Elektromagnetische Lichttheorie," in Handbuch der Physik (Springer, Berlin, 1928), Vol. XX.

R. Minkowski, "Theorie der Reflexion, Brechung und Dispersion," in Müller-Pouillet's Lehrbuch der Physik (Friedr. Vieweg und Sohn Akt. Ges., Braunschweig, 1929).

Julius A. Stratton, Electromagnetic Theory (McGraw-Hill Book Company, Inc., New York, 1941).

Max Born and Emil Wolf, Principles of Optics (Pergamon Press, New York, 1959).

Richard Tousey, J. Opt. Soc. Am. 29, 235 (1939).

Parry Moon, J. Math. Phys. 19, 1 (1940).

Ivan Šimon, J. Opt. Soc. Am. 41, 336 (1951).

D. G. Avery, Proc. Phys. Soc. (London) 65, 425 (1952).

Gerhard Heilmann, Physik 152, 368 (1958).

Kozo Ishiguro, Taizo Sasaki, and Sadao Nomura, Sci. Papers of the College of General Education, University of Tokyo 10, 207 (1960).

S. P. F. Humphreys-Owen, Proc. Phys. Soc. (London) 77, 949 (1961).

H. G. Häfele, Physik 168, 530 (1962).

A. P. Prishivalko, Reflection of Light from Absorbing Media (Academy of Sciences of White Russian SSR, Minsk, 1963).

Antonín Vašiček, Tables of Determination of Optical Constants from the Intensities of Reflected Light (Nakladatelství Ceskoslovenskí Akademie VĚD, Praha, 1964).

The information about Dr. A. P. Prishivalko's work was furnished by Professor Dr. Antonín Vašiček, University Brno, Czeckoslavakia, who also supplied a copy of the former's book which contained the tables. The author is deeply indebted to Dr. Vašíček for these kindnesses.

Background details and complete sequence of equations on which this discussion is based can be found in Ref. 2.

Expressions for the first and second Brewster angles can be obtained by differentiation of expressions based on Eqs. (2) and (3). To do this, however, requires tedious analytical labor, and it has previously been considered impossible to solve this problem explicitly (Refs. 20, 21) so that only approximations were sought. The problem found new consideration recently, and was explicitly solved for the first Brewster angle by Humphreys-Owen13 and for the second Brewster angle by Potter.22

C. Boeckner, J. Opt. Soc. Am. and Rev. Sci. Instr. 19, 7 (1929).

P. H. Miller, Jr., and J. R. Johnson, Physica 20, 11, 1026 (1954).

Roy F. Potter, J. Opt. Soc. Am. 54, 904 (1964).

These tables were for internal use only and were not published in Holl.2

Paul Drude, The Theory of Optics (Dover Publications, Inc., New York, 1959).

A similar equation given by König3 [Eq. (169b), p. 246] is found to be incorrect.

Herbert B. Holl, Numerical Solutions of the Fresnel Equations in the Optical Region, Symposium on Thermal Radiation of Solids, NASA SP-55, AF ML-TDR-64-159 (National Aeronautics & Space Administration, Washington, D. C, 1965), p. 45.

R. W. Wood, Phys. Rev. 44, 353 (1933).

R. de L. Kronig [Nature, Feb. 10, 211 (1934)] obtained, for potassium, N = 0.294–0.0058i for λ = 2727 Å.

Felix Jentzsch-Gräfe [Verhandl. Deut. Phys. Ges. 21, 361, (1919)] thoroughly investigated the minimum reflectance of natural light for real index of refraction. His paper presented an exact mathematical formulation for this case and tabulated the values for θ0 and R=min from n=3.7321 to n=9.507.

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