Abstract

By consideration of the formulae for the reflection and transmission of up to three films, it has been possible to form a generalization for an arbitrary number of films. This generalization is stated as a simple rule whereby the expressions for the reflected and transmitted amplitudes can be readily formed in terms of the Fresnel coefficients of the various boundaries. The generalization is proved by induction. It is also shown that the solutions of the problem by the consideration of the electromagnetic disturbance in each medium, and by the summation of multiple beams, lead to the same result.

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  1. Lord Rayleigh, Scientific Papers (Cambridge University Press, Teddington, England, 1902), Vol. 3, p. 63.
  2. P. Drude, Theory of Optics (Longmans Green and Company, New York, 1902), p. 302.
  3. T. C. Fry, J. Opt. Soc. Am. 16, 1 (1928).
  4. J. B. Nathanson and C. L. Bartberger, J. Opt. Soc. Am. 29, 417 (1939).
  5. C. E. Leberknight and B. Lustman, J. Opt. Soc. Am. 29, 59 (1939).
  6. K. B. Blodgett, Phys. Rev. 57, 921 (1940).
  7. J. A. Stratton, Electro Magnetic Theory (McGraw-Hill Book Company, Inc., New York, 1941), p. 511.
  8. K. M. Greenland, Nature 152, 290 (1943).
  9. A. B. Winterbottom, Trans. Faraday Soc. 42, 478 (1946).
  10. A. Vašiček, J. Opt. Soc. Am. 37, 145 (1947).
  11. P. King and L. B. Lockhart, J. Opt. Soc. Am. 36, 513 (1946).
  12. R. Messner, Optik 2, 228 (1947).
  13. L. B. Lockhart and P. King, J. Opt. Soc. Am. 36, 689 (1947).
  14. L. N. Hadley and D. M. Dennison, J. Opt. Soc. Am. 37, 451 (1947).
  15. R. L. Mooney, J. Opt. Soc. Am. 35, 574 (1945).
  16. D. L. Caballero, J. Opt. Soc. Am. 37, 176 (1947).
  17. W. Weinstein, J. Opt. Soc. Am. 37, 576 (1947).
  18. A. Herpin, Comptes Rendus 225, 182 (1947).
  19. A. Vašiček, J. Opt. Soc. Am. 37, 623 (1947).
  20. See reference 2, p. 296.
  21. R. W. Wood, Physical Optics (MacMillan Company, Ltd., London, 1939), third edition, p. 416.
  22. W. König, Handbuch der Physik 20, 229 (1928).
  23. $ee reference 1, p. 67,

Bartberger, C. L.

J. B. Nathanson and C. L. Bartberger, J. Opt. Soc. Am. 29, 417 (1939).

Blodgett, K. B.

K. B. Blodgett, Phys. Rev. 57, 921 (1940).

Caballero, D. L.

D. L. Caballero, J. Opt. Soc. Am. 37, 176 (1947).

Dennison, D. M.

L. N. Hadley and D. M. Dennison, J. Opt. Soc. Am. 37, 451 (1947).

Drude, P.

P. Drude, Theory of Optics (Longmans Green and Company, New York, 1902), p. 302.

Fry, T. C.

T. C. Fry, J. Opt. Soc. Am. 16, 1 (1928).

Greenland, K. M.

K. M. Greenland, Nature 152, 290 (1943).

Hadley, L. N.

L. N. Hadley and D. M. Dennison, J. Opt. Soc. Am. 37, 451 (1947).

Herpin, A.

A. Herpin, Comptes Rendus 225, 182 (1947).

King, P.

P. King and L. B. Lockhart, J. Opt. Soc. Am. 36, 513 (1946).

L. B. Lockhart and P. King, J. Opt. Soc. Am. 36, 689 (1947).

König, W.

W. König, Handbuch der Physik 20, 229 (1928).

Leberknight, C. E.

C. E. Leberknight and B. Lustman, J. Opt. Soc. Am. 29, 59 (1939).

Lockhart, L. B.

P. King and L. B. Lockhart, J. Opt. Soc. Am. 36, 513 (1946).

L. B. Lockhart and P. King, J. Opt. Soc. Am. 36, 689 (1947).

Lustman, B.

C. E. Leberknight and B. Lustman, J. Opt. Soc. Am. 29, 59 (1939).

Messner, R.

R. Messner, Optik 2, 228 (1947).

Mooney, R. L.

R. L. Mooney, J. Opt. Soc. Am. 35, 574 (1945).

Nathanson, J. B.

J. B. Nathanson and C. L. Bartberger, J. Opt. Soc. Am. 29, 417 (1939).

Rayleigh, Lord

Lord Rayleigh, Scientific Papers (Cambridge University Press, Teddington, England, 1902), Vol. 3, p. 63.

Stratton, J. A.

J. A. Stratton, Electro Magnetic Theory (McGraw-Hill Book Company, Inc., New York, 1941), p. 511.

Vašicek, A.

A. Vašiček, J. Opt. Soc. Am. 37, 145 (1947).

A. Vašiček, J. Opt. Soc. Am. 37, 623 (1947).

Weinstein, W.

W. Weinstein, J. Opt. Soc. Am. 37, 576 (1947).

Winterbottom, A. B.

A. B. Winterbottom, Trans. Faraday Soc. 42, 478 (1946).

Wood, R. W.

R. W. Wood, Physical Optics (MacMillan Company, Ltd., London, 1939), third edition, p. 416.

Other

Lord Rayleigh, Scientific Papers (Cambridge University Press, Teddington, England, 1902), Vol. 3, p. 63.

P. Drude, Theory of Optics (Longmans Green and Company, New York, 1902), p. 302.

T. C. Fry, J. Opt. Soc. Am. 16, 1 (1928).

J. B. Nathanson and C. L. Bartberger, J. Opt. Soc. Am. 29, 417 (1939).

C. E. Leberknight and B. Lustman, J. Opt. Soc. Am. 29, 59 (1939).

K. B. Blodgett, Phys. Rev. 57, 921 (1940).

J. A. Stratton, Electro Magnetic Theory (McGraw-Hill Book Company, Inc., New York, 1941), p. 511.

K. M. Greenland, Nature 152, 290 (1943).

A. B. Winterbottom, Trans. Faraday Soc. 42, 478 (1946).

A. Vašiček, J. Opt. Soc. Am. 37, 145 (1947).

P. King and L. B. Lockhart, J. Opt. Soc. Am. 36, 513 (1946).

R. Messner, Optik 2, 228 (1947).

L. B. Lockhart and P. King, J. Opt. Soc. Am. 36, 689 (1947).

L. N. Hadley and D. M. Dennison, J. Opt. Soc. Am. 37, 451 (1947).

R. L. Mooney, J. Opt. Soc. Am. 35, 574 (1945).

D. L. Caballero, J. Opt. Soc. Am. 37, 176 (1947).

W. Weinstein, J. Opt. Soc. Am. 37, 576 (1947).

A. Herpin, Comptes Rendus 225, 182 (1947).

A. Vašiček, J. Opt. Soc. Am. 37, 623 (1947).

See reference 2, p. 296.

R. W. Wood, Physical Optics (MacMillan Company, Ltd., London, 1939), third edition, p. 416.

W. König, Handbuch der Physik 20, 229 (1928).

$ee reference 1, p. 67,

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