Abstract

Deviations from Lamberts cosine law for the light emitted by W, Mo, and Ta. The deviations for all three metals is very much of the same order. The brightness in each instance increases from the normal value at normal emergence gradually with increase in emergence angle to about 75° by about 20 per cent. From there on the brightness decreases rapidly to zero at grazing emergence. Straight filaments of circular cross-section have average brightnesses viewed normal to their axes which are about 3 per cent greater than the normal brightnesses (W 2.8 per cent, Mo 3.6 per cent, Ta 2.7 per cent). The average brightness of a filament, considering all directions, is about 5 per cent greater than the normal brightness (W 4.4 per cent, Mo 6.2 per cent, Ta 4.3 per cent).

Polarization of light emitted by W, Mo, and Ta. The light emitted by these materials starting with zero polarization for normal emergence increases with the angle of emergence, at first slowly, to about 95 per cent at grazing emergence. The polarizations of the light from straight filaments of circular cross-section viewed normal to their axes amount to about 20 per cent (W 19.3 per cent, Mo 20.8 per cent, Ta 18.5 per cent).

Change in optical constants of tungsten with temperature. Values obtained have depended on the variations of the emissivity and the reflectivity for the two polarized components. At room temperature 3.86 and.81 were obtained for n and k, at 1900°K 3.85 and.89 were obtained. This difference checks well with observed values of emissivity for normal emergence.

© 1926 Optical Society of America

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References

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  1. Worthing, Astrophysical Journal 36, p. 345; 1912.
    [Crossref]
  2. Provostaye and Desains, Ann. Chim. Phys.,  32, p. 112; 1851. Möller, Ann. Phys.,  24, p. 266; 1885. Violle, Compt. Rend.,  105, p. 111; 1886. Millikan, Phys. Rev.,  3, p. 81 and p. 177;1895. Uljamin, Ann. Phys.,  62, p. 528; 1897.
    [Crossref]
  3. Laue and Martens, Physik. ZS. 8, p. 853; 1907.
  4. Forsythe and Worthing, Astrophys. J.,  61, p. 146; 1925.
    [Crossref]
  5. Worthing, Phys. Rev. 25, p. 846, 1925;Phys. Rev. 28, p. 174, 1926.
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    [Crossref]
  7. Millikan, Phys. Rev.,  3, p. 81 and p. 177; 1895.
  8. Laue and Martens, Physik. ZS.,  8, p. 853; 1907.
  9. Holborn and Henning, Berl. Ber.,  311, 1905. Henning, Z. Instrumentenk.,  30, p. 61; 1910. Pirani and Meyer, Elektrotech. u. Mashinenbau,  33, p. 397 and p. 414; 1915. Henning and Heuse, ZS. f. Physik,  16, p. 63; 1923. Lax and Pirani, ZS. f. Physik,  22, p. 275; 1924.
    [Crossref]
  10. Hyde, Astrophys. J.,  36, p. 89; 1912. Mendenhall and Forsythe, Astrophys. J.,  37, p. 380; 1913. McCauley, Astrophys. J.,  37, p. 164; 1913. Burgess and Watterberg, Bull. Bur. Stds.,  11, p. 591; 1914. Worthing, J. Frank. Inst.,  181, 417, 1916;Phys. Rev.,  10, p. 377, 1917;Phys. Rev.,  25, 846, 1925;Phys. Rev. 28, 174, 1926;Z. Physik,  22, p. 9; 1924. Shackelford, Phys. Rev.,  8, p. 470; 1916. Hulburt, Astrophys. J.,  45, p. 149; 1917. Weniger and Pfund, Phys. Rev.,  14, p. 427; 1919. Zwikker, Arch. Neerland.,  9, p. 207; 1925. Ebeling, ZS. f. Physik,  32, p. 489; 1925.
    [Crossref]
  11. Worthing, loc. cit, Phys. Rev.,  10, p. 377; 1917; Forsythe and Worthing, Astrophys. J.,  61, p. 146; 1925.
    [Crossref]

1925 (2)

Forsythe and Worthing, Astrophys. J.,  61, p. 146; 1925.
[Crossref]

Worthing, Phys. Rev. 25, p. 846, 1925;Phys. Rev. 28, p. 174, 1926.
[Crossref]

1917 (1)

Worthing, loc. cit, Phys. Rev.,  10, p. 377; 1917; Forsythe and Worthing, Astrophys. J.,  61, p. 146; 1925.
[Crossref]

1912 (2)

Hyde, Astrophys. J.,  36, p. 89; 1912. Mendenhall and Forsythe, Astrophys. J.,  37, p. 380; 1913. McCauley, Astrophys. J.,  37, p. 164; 1913. Burgess and Watterberg, Bull. Bur. Stds.,  11, p. 591; 1914. Worthing, J. Frank. Inst.,  181, 417, 1916;Phys. Rev.,  10, p. 377, 1917;Phys. Rev.,  25, 846, 1925;Phys. Rev. 28, 174, 1926;Z. Physik,  22, p. 9; 1924. Shackelford, Phys. Rev.,  8, p. 470; 1916. Hulburt, Astrophys. J.,  45, p. 149; 1917. Weniger and Pfund, Phys. Rev.,  14, p. 427; 1919. Zwikker, Arch. Neerland.,  9, p. 207; 1925. Ebeling, ZS. f. Physik,  32, p. 489; 1925.
[Crossref]

Worthing, Astrophysical Journal 36, p. 345; 1912.
[Crossref]

1907 (2)

Laue and Martens, Physik. ZS. 8, p. 853; 1907.

Laue and Martens, Physik. ZS.,  8, p. 853; 1907.

1905 (1)

Holborn and Henning, Berl. Ber.,  311, 1905. Henning, Z. Instrumentenk.,  30, p. 61; 1910. Pirani and Meyer, Elektrotech. u. Mashinenbau,  33, p. 397 and p. 414; 1915. Henning and Heuse, ZS. f. Physik,  16, p. 63; 1923. Lax and Pirani, ZS. f. Physik,  22, p. 275; 1924.
[Crossref]

1895 (1)

Millikan, Phys. Rev.,  3, p. 81 and p. 177; 1895.

1889 (1)

Kundt, Wied. Ann.,  36, p. 834; 1889. Drude, Wied. Ann.,  39, p. 538; 1890. Sissingh, Arch. Neerland., tome  XX. Zeeman, Com. Phys. Lab. Leyden,  20; 1895. Pfleuger, Wied. Ann.,  58, p. 483; 1896. Kent, Phys. Rev.,  14, p. 495; 1919. Aster, Phys. Rev.,  20, p. 349.
[Crossref]

1851 (1)

Provostaye and Desains, Ann. Chim. Phys.,  32, p. 112; 1851. Möller, Ann. Phys.,  24, p. 266; 1885. Violle, Compt. Rend.,  105, p. 111; 1886. Millikan, Phys. Rev.,  3, p. 81 and p. 177;1895. Uljamin, Ann. Phys.,  62, p. 528; 1897.
[Crossref]

Desains,

Provostaye and Desains, Ann. Chim. Phys.,  32, p. 112; 1851. Möller, Ann. Phys.,  24, p. 266; 1885. Violle, Compt. Rend.,  105, p. 111; 1886. Millikan, Phys. Rev.,  3, p. 81 and p. 177;1895. Uljamin, Ann. Phys.,  62, p. 528; 1897.
[Crossref]

Forsythe,

Forsythe and Worthing, Astrophys. J.,  61, p. 146; 1925.
[Crossref]

Henning,

Holborn and Henning, Berl. Ber.,  311, 1905. Henning, Z. Instrumentenk.,  30, p. 61; 1910. Pirani and Meyer, Elektrotech. u. Mashinenbau,  33, p. 397 and p. 414; 1915. Henning and Heuse, ZS. f. Physik,  16, p. 63; 1923. Lax and Pirani, ZS. f. Physik,  22, p. 275; 1924.
[Crossref]

Holborn,

Holborn and Henning, Berl. Ber.,  311, 1905. Henning, Z. Instrumentenk.,  30, p. 61; 1910. Pirani and Meyer, Elektrotech. u. Mashinenbau,  33, p. 397 and p. 414; 1915. Henning and Heuse, ZS. f. Physik,  16, p. 63; 1923. Lax and Pirani, ZS. f. Physik,  22, p. 275; 1924.
[Crossref]

Hyde,

Hyde, Astrophys. J.,  36, p. 89; 1912. Mendenhall and Forsythe, Astrophys. J.,  37, p. 380; 1913. McCauley, Astrophys. J.,  37, p. 164; 1913. Burgess and Watterberg, Bull. Bur. Stds.,  11, p. 591; 1914. Worthing, J. Frank. Inst.,  181, 417, 1916;Phys. Rev.,  10, p. 377, 1917;Phys. Rev.,  25, 846, 1925;Phys. Rev. 28, 174, 1926;Z. Physik,  22, p. 9; 1924. Shackelford, Phys. Rev.,  8, p. 470; 1916. Hulburt, Astrophys. J.,  45, p. 149; 1917. Weniger and Pfund, Phys. Rev.,  14, p. 427; 1919. Zwikker, Arch. Neerland.,  9, p. 207; 1925. Ebeling, ZS. f. Physik,  32, p. 489; 1925.
[Crossref]

Kundt,

Kundt, Wied. Ann.,  36, p. 834; 1889. Drude, Wied. Ann.,  39, p. 538; 1890. Sissingh, Arch. Neerland., tome  XX. Zeeman, Com. Phys. Lab. Leyden,  20; 1895. Pfleuger, Wied. Ann.,  58, p. 483; 1896. Kent, Phys. Rev.,  14, p. 495; 1919. Aster, Phys. Rev.,  20, p. 349.
[Crossref]

Laue,

Laue and Martens, Physik. ZS. 8, p. 853; 1907.

Laue and Martens, Physik. ZS.,  8, p. 853; 1907.

Martens,

Laue and Martens, Physik. ZS.,  8, p. 853; 1907.

Laue and Martens, Physik. ZS. 8, p. 853; 1907.

Millikan,

Millikan, Phys. Rev.,  3, p. 81 and p. 177; 1895.

Provostaye,

Provostaye and Desains, Ann. Chim. Phys.,  32, p. 112; 1851. Möller, Ann. Phys.,  24, p. 266; 1885. Violle, Compt. Rend.,  105, p. 111; 1886. Millikan, Phys. Rev.,  3, p. 81 and p. 177;1895. Uljamin, Ann. Phys.,  62, p. 528; 1897.
[Crossref]

Worthing,

Forsythe and Worthing, Astrophys. J.,  61, p. 146; 1925.
[Crossref]

Worthing, Phys. Rev. 25, p. 846, 1925;Phys. Rev. 28, p. 174, 1926.
[Crossref]

Worthing, loc. cit, Phys. Rev.,  10, p. 377; 1917; Forsythe and Worthing, Astrophys. J.,  61, p. 146; 1925.
[Crossref]

Worthing, Astrophysical Journal 36, p. 345; 1912.
[Crossref]

Ann. Chim. Phys. (1)

Provostaye and Desains, Ann. Chim. Phys.,  32, p. 112; 1851. Möller, Ann. Phys.,  24, p. 266; 1885. Violle, Compt. Rend.,  105, p. 111; 1886. Millikan, Phys. Rev.,  3, p. 81 and p. 177;1895. Uljamin, Ann. Phys.,  62, p. 528; 1897.
[Crossref]

Astrophys. J. (2)

Forsythe and Worthing, Astrophys. J.,  61, p. 146; 1925.
[Crossref]

Hyde, Astrophys. J.,  36, p. 89; 1912. Mendenhall and Forsythe, Astrophys. J.,  37, p. 380; 1913. McCauley, Astrophys. J.,  37, p. 164; 1913. Burgess and Watterberg, Bull. Bur. Stds.,  11, p. 591; 1914. Worthing, J. Frank. Inst.,  181, 417, 1916;Phys. Rev.,  10, p. 377, 1917;Phys. Rev.,  25, 846, 1925;Phys. Rev. 28, 174, 1926;Z. Physik,  22, p. 9; 1924. Shackelford, Phys. Rev.,  8, p. 470; 1916. Hulburt, Astrophys. J.,  45, p. 149; 1917. Weniger and Pfund, Phys. Rev.,  14, p. 427; 1919. Zwikker, Arch. Neerland.,  9, p. 207; 1925. Ebeling, ZS. f. Physik,  32, p. 489; 1925.
[Crossref]

Astrophysical Journal (1)

Worthing, Astrophysical Journal 36, p. 345; 1912.
[Crossref]

Berl. Ber. (1)

Holborn and Henning, Berl. Ber.,  311, 1905. Henning, Z. Instrumentenk.,  30, p. 61; 1910. Pirani and Meyer, Elektrotech. u. Mashinenbau,  33, p. 397 and p. 414; 1915. Henning and Heuse, ZS. f. Physik,  16, p. 63; 1923. Lax and Pirani, ZS. f. Physik,  22, p. 275; 1924.
[Crossref]

loc. cit, Phys. Rev. (1)

Worthing, loc. cit, Phys. Rev.,  10, p. 377; 1917; Forsythe and Worthing, Astrophys. J.,  61, p. 146; 1925.
[Crossref]

Phys. Rev. (2)

Millikan, Phys. Rev.,  3, p. 81 and p. 177; 1895.

Worthing, Phys. Rev. 25, p. 846, 1925;Phys. Rev. 28, p. 174, 1926.
[Crossref]

Physik. ZS. (2)

Laue and Martens, Physik. ZS. 8, p. 853; 1907.

Laue and Martens, Physik. ZS.,  8, p. 853; 1907.

Wied. Ann. (1)

Kundt, Wied. Ann.,  36, p. 834; 1889. Drude, Wied. Ann.,  39, p. 538; 1890. Sissingh, Arch. Neerland., tome  XX. Zeeman, Com. Phys. Lab. Leyden,  20; 1895. Pfleuger, Wied. Ann.,  58, p. 483; 1896. Kent, Phys. Rev.,  14, p. 495; 1919. Aster, Phys. Rev.,  20, p. 349.
[Crossref]

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Figures (6)

F. 1
F. 1

S is a nearly enclosed light source, M a lamp containing a ribbon filament whose reflectivity is to be measured, Q a rochon double image prism, L a lens imaging S on the ribbon filament, P a disappearing filament pyrometer with pyrometer lamp at l, absorbing screen at a, limiting diaphragm at d, and colored pyrometer glass filter at f. S, L, and M are supported on a rotatable mount with a vertical axis at the center of M. S′ and L′ are positions corresponding to S and L for the determination of the unreflected brightness of the image of S. The locations of adjusting devices and of pinhole diaphragms for alignment testing are not shown.

F. 2
F. 2

Relative brightnesses for the principal polarized light components B and B and the natural light B+B, and the polarization of the natural light P emitted by tungsten at incandescence as functions of the angle of emission. 1750 ° K 1950 ° K × } 2470 ° K .

F. 3
F. 3

Relative brightnesses for the principal polarized light components B and B and the natural light B+B, and the polarization of the natural light P emitted by molybdenum at 2155°K as functions of the angle of emission. The ordinates of the B+B curve are the sums of the ordinates of the B and the B curves.

F. 4
F. 4

Relative brightnesses for the principal polarized light components B and B and the natural light B+B, and the polarization of the natural light P emitted by tantalum at 1650°K as functions of the angle of emission. The ordinates of the full line curve B+B are the sums of the ordinates of the B and the B curves.

F. 5
F. 5

Relative brightness of the natural light emitted by straight incandescent filaments of circular cross-section of tungsten, molybdenum and tantalum as a function of the projected distance from the filament axis when viewed normally to the axis of the filament.

F. 6
F. 6

Polarization produced by reflection from tungsten at room temperature for angles of incidence approximating the angle of principal incidence.

Tables (2)

Tables Icon

Table 1 Showing for tungsten, molybdenum, and tantalum θm the angle of emission at which a filament is brightest, Bm/B0 the ratio of that brightness to the normal brightness, (Bav/B0)1 the ratio of the average brightness for a cylindrical filament of circular cross-section viewed normal to that axis to its normal brightness, (Bav/B0)2 the ratio of the average brightness of a portion of the material as viewed from all directions to its normal brightness, and P the polarization of the light from a straight filament of circular cross-section taken as a whole.

Tables Icon

Table 2 Data leading to and results for the optical constants of tungsten for various temperatures (λ=0.665μ)

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

2 π 0 π / 2 B θ sin θ cos θ d θ 2 π 0 π / 2 sin θ cos θ d θ ,
[ tan 2 ψ = R R ] ϕ = Φ
n = sin Φ tan Φ 1 + k 2 [ 1 1 2 sin 2 Φ n 2 ( 1 + k 2 ) 1 k 2 1 + k 2 ] k = tan 2 ψ 1 + sin 2 Φ n 2 ( 1 + k 2 )
e n = 1 n 2 ( 1 + k 2 ) 2 n + 1 n 2 ( 1 + k 2 ) + 2 n + 1 .
1750 ° K 1950 ° K × } 2470 ° K .