Abstract

The reflectivities of Ag, Au, Cu, and Al were measured at an angle of incidence of 45°, in the wavelength range of 0.40μ to 0.95μ at glass-metal and air-metal interfaces. These reflectivities, together with previously determined values of the absorption coefficient k, were used to calculate the index of refraction n. Samples were prepared by evaporation and deposition from the vapor. The important experimental results are: (1) The ratios of the reflectivities in the s plane to those in the p plane agreed with the theoretical values. This result indicates that the boundary conditions required for the application of the equations of electromagnetic theory have been satisfied. (2) Ageing and annealing resulted in increased reflectivity at both air-metal and glass-metal interfaces. (3) The values of n obtained from aged or annealed samples were in many cases considerably lower than previously published values.

© 1954 Optical Society of America

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References

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  1. W. König, Handbuch der Physik (Verlag Julius Springer, Berlin, 1928), Vol. 20, Chap. 6.
  2. L. G. Schulz, J. Opt. Soc. Am. 44, 357 (1954).
    [CrossRef]
  3. C. F. E. Simons, Physica 10, 141 (1943).
    [CrossRef]
  4. F. Seitz, Modern Theory of Solids (McGraw-Hill Book Company, Inc., New York, 1941), Chap. 17.
  5. N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys (Oxford University Press, New York, 1936), Chap. 3.
  6. A. H. Wilson, Theory of Metals (Cambridge University Press, Cambridge, 1946), Chap. 3.
  7. R. S. Sennett and G. D. Scott, J. Opt. Soc. Am. 40, 203 (1950).
    [CrossRef]
  8. W. West, Physical Methods of Organic Chemistry, edited by Arnold Weissberger (Interscience Publishers, Inc., New York, 1946), p. 852.
  9. John Strong, Procedures in Experimental Physics (Prentice-Hall, Inc., New York, 1938), Chap. 9.
  10. H. H. Carey and A. O. Beckman, J. opt. Soc. Am. 31, 682 (1941).
    [CrossRef]
  11. P. G. Wilkinson and L. S. Birks, J. Appl. Phys. 20, 1168 (1949).
    [CrossRef]
  12. Eber Halteman, J. Appl. Phys. 23, 150 (1952).
    [CrossRef]
  13. R. Suhrman and G. Barth, Z. Physik 103, 157 (1936).
    [CrossRef]
  14. R. Kretzmann, Ann. Physik 37, 303 (1940).
    [CrossRef]
  15. Georg Hass, Optik 1, 2 (1946).
  16. Lowery, Wilkinson, and Smare, Phil. Mag. 22, 769 (1936).
  17. A. Q. Tool, Phys. Rev. 31, 1 (1910).
  18. W. Meier, Ann. Physik 31, 1017 (1910).
    [CrossRef]
  19. H. O’Bryan, J. Opt. Soc. Am. 26, 122 (1936).
    [CrossRef]

1954 (1)

1952 (1)

Eber Halteman, J. Appl. Phys. 23, 150 (1952).
[CrossRef]

1950 (1)

1949 (1)

P. G. Wilkinson and L. S. Birks, J. Appl. Phys. 20, 1168 (1949).
[CrossRef]

1946 (1)

Georg Hass, Optik 1, 2 (1946).

1943 (1)

C. F. E. Simons, Physica 10, 141 (1943).
[CrossRef]

1941 (1)

1940 (1)

R. Kretzmann, Ann. Physik 37, 303 (1940).
[CrossRef]

1936 (3)

R. Suhrman and G. Barth, Z. Physik 103, 157 (1936).
[CrossRef]

Lowery, Wilkinson, and Smare, Phil. Mag. 22, 769 (1936).

H. O’Bryan, J. Opt. Soc. Am. 26, 122 (1936).
[CrossRef]

1910 (2)

A. Q. Tool, Phys. Rev. 31, 1 (1910).

W. Meier, Ann. Physik 31, 1017 (1910).
[CrossRef]

Barth, G.

R. Suhrman and G. Barth, Z. Physik 103, 157 (1936).
[CrossRef]

Beckman, A. O.

Birks, L. S.

P. G. Wilkinson and L. S. Birks, J. Appl. Phys. 20, 1168 (1949).
[CrossRef]

Carey, H. H.

Halteman, Eber

Eber Halteman, J. Appl. Phys. 23, 150 (1952).
[CrossRef]

Hass, Georg

Georg Hass, Optik 1, 2 (1946).

Jones, H.

N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys (Oxford University Press, New York, 1936), Chap. 3.

König, W.

W. König, Handbuch der Physik (Verlag Julius Springer, Berlin, 1928), Vol. 20, Chap. 6.

Kretzmann, R.

R. Kretzmann, Ann. Physik 37, 303 (1940).
[CrossRef]

Lowery,

Lowery, Wilkinson, and Smare, Phil. Mag. 22, 769 (1936).

Meier, W.

W. Meier, Ann. Physik 31, 1017 (1910).
[CrossRef]

Mott, N. F.

N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys (Oxford University Press, New York, 1936), Chap. 3.

O’Bryan, H.

Schulz, L. G.

Scott, G. D.

Seitz, F.

F. Seitz, Modern Theory of Solids (McGraw-Hill Book Company, Inc., New York, 1941), Chap. 17.

Sennett, R. S.

Simons, C. F. E.

C. F. E. Simons, Physica 10, 141 (1943).
[CrossRef]

Smare,

Lowery, Wilkinson, and Smare, Phil. Mag. 22, 769 (1936).

Strong, John

John Strong, Procedures in Experimental Physics (Prentice-Hall, Inc., New York, 1938), Chap. 9.

Suhrman, R.

R. Suhrman and G. Barth, Z. Physik 103, 157 (1936).
[CrossRef]

Tool, A. Q.

A. Q. Tool, Phys. Rev. 31, 1 (1910).

West, W.

W. West, Physical Methods of Organic Chemistry, edited by Arnold Weissberger (Interscience Publishers, Inc., New York, 1946), p. 852.

Wilkinson,

Lowery, Wilkinson, and Smare, Phil. Mag. 22, 769 (1936).

Wilkinson, P. G.

P. G. Wilkinson and L. S. Birks, J. Appl. Phys. 20, 1168 (1949).
[CrossRef]

Wilson, A. H.

A. H. Wilson, Theory of Metals (Cambridge University Press, Cambridge, 1946), Chap. 3.

Ann. Physik (2)

R. Kretzmann, Ann. Physik 37, 303 (1940).
[CrossRef]

W. Meier, Ann. Physik 31, 1017 (1910).
[CrossRef]

J. Appl. Phys. (2)

P. G. Wilkinson and L. S. Birks, J. Appl. Phys. 20, 1168 (1949).
[CrossRef]

Eber Halteman, J. Appl. Phys. 23, 150 (1952).
[CrossRef]

J. Opt. Soc. Am. (3)

Optik (1)

Georg Hass, Optik 1, 2 (1946).

Phil. Mag. (1)

Lowery, Wilkinson, and Smare, Phil. Mag. 22, 769 (1936).

Phys. Rev. (1)

A. Q. Tool, Phys. Rev. 31, 1 (1910).

Physica (1)

C. F. E. Simons, Physica 10, 141 (1943).
[CrossRef]

Z. Physik (1)

R. Suhrman and G. Barth, Z. Physik 103, 157 (1936).
[CrossRef]

Other (6)

F. Seitz, Modern Theory of Solids (McGraw-Hill Book Company, Inc., New York, 1941), Chap. 17.

N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys (Oxford University Press, New York, 1936), Chap. 3.

A. H. Wilson, Theory of Metals (Cambridge University Press, Cambridge, 1946), Chap. 3.

W. König, Handbuch der Physik (Verlag Julius Springer, Berlin, 1928), Vol. 20, Chap. 6.

W. West, Physical Methods of Organic Chemistry, edited by Arnold Weissberger (Interscience Publishers, Inc., New York, 1946), p. 852.

John Strong, Procedures in Experimental Physics (Prentice-Hall, Inc., New York, 1938), Chap. 9.

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Figures (8)

F. 1
F. 1

Drawings showing the optical path through the samples. The prisms of (A) and (B) were placed close to one another but not in optical contact. The glass blocks of (C) and (D) are shown with four internal reflections in each, but they could also be turned to give two or six reflections in each. These blocks were 4 in . × 1 in . × 7 8 in. The sample of F labeled I-II-III-IV was formed from the four prisms used in (A) and (B). The square face of each prism was 1.25 in. on an edge.

F. 2
F. 2

Drawing showing how the sample, S or S′, was inserted into the Pulfrich photometer. A Nicol prism N mounted beyond the eyepiece E made it possible to measure separately the reflectivity in the s and p planes. The polaroid, P or P′, was inserted only when testing the sample or the photometer for stray polarization effects. F indicates the position at which the various filters could be placed.

F. 3
F. 3

Graph showing the values of ΔR as a function of n and k. The numbers on the curves indicate the k values. Note that the vertical scale for the positive ΔR region is different from that for the negative region. The calculations are for a vacuum-metal interface. To use the graph for the case of a dielectric other than vacuum, n and k must be normalized, that is, divided by the index of refraction of the dielectric.

F. 4
F. 4

Graph showing the variation in reflectivities with changing angle of incidence for a particular set of values for k, n, and n0. Note that at 45° the value of Rs2 is equal to Rp.

F. 5
F. 5

Graph showing the corrections for the errors due to multiple reflections between the prisms. Δ R ¯ and Δ(Rp2/Rs) are to be added to the experimental values of R ¯ and Rs2/Rp, respectively. Included on the graph is the fractional error in R ¯. (This graph is for the case of a 4-prism sample with all prisms metallized.)

F. 6
F. 6

Graph (A) shows various n values for a Ag sample together with the results of two older measurements. Graphs (B) and (C) show Rs/Rp values for the same sample.

F. 7
F. 7

Graph (A) shows various n values for one of the Cu samples. Graphs (B) and (C) show the Rs2/Rp values for the air-metal interfaces of samples of Pb and Sn respectively.

F. 8
F. 8

Values of n for Ag, Au, Cu, and Al. It is interesting to compare the dispersion shown here in the n values with that of the k values shown in Figs. 47 of Part I.

Tables (1)

Tables Icon

Table I Values of the index of refraction n for Ag, Au, Cu and Al. These values are based on glass-metal reflectivities measured with a Beckman spectrophotometer on samples which had been annealed or aged and which satisfied the condition Rs2 = Rp. The number of samples (a sample consists of 4 metallized prisms) for each metal was as follows: For Ag, 4; for Au, 2; for Cu, 2; and for Al, 4.

Equations (6)

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R s = a 2 + b 2 2 a cos i + cos 2 i a 2 + b 2 + 2 a cos i + cos 2 i ,
R p = R s a 2 + b 2 2 a sin i tan i + sin 2 i tan 2 i a 2 + b 2 + 2 a sin i tan i + sin 2 i tan 2 i .
a 2 = 1 2 n 0 2 { [ ( n 2 k 2 n 0 2 sin 2 i ) 2 + 4 n 2 k 2 ] 1 2 + n 2 k 2 n 0 2 sin 2 i } ,
b 2 = 1 2 n 0 2 { [ ( n 2 k 2 n 0 2 sin 2 i ) 2 + 4 n 2 k 2 ] 1 2 n 2 + k 2 + n 0 2 sin 2 i } .
R 0 = k 2 + ( n 0 n ) 2 k 2 + ( n 0 + n ) 2 .
R 0 = 1 4 n 0 n / k 2 .