Abstract

Many spectrophotometers utilize polarizing prisms and determine the reflection factor of the sample by plane polarized light. In general, the reflection factor of the sample is independent of the azimuth of the plane of polarization but there are some materials, notably textiles, for which the reflection factor depends upon the azimuth. It can be shown mathematically that, if the reflection factor is determined for two azimuths at right angles to one another, the arithmetic average of the two values is the reflection factor for ordinary, or unpolarized light. This is true regardless of the azimuths selected. Experimental data are presented which indicate the applicability of this principle to the measurement of the color of textile fabrics.

© 1935 Optical Society of America

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References

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  1. R. D. Nutting, J. Opt. Soc. Am. 24, 135 (1934).
    [CrossRef]
  2. H. J. McNicholas, Bur. Standards J. Research 1, 793 (1928).
    [CrossRef]
  3. W. D. Appel, Am. Dyestuff Reptr. 17, 49 (1928).
  4. E. M. Shelton and R. L. Emerson, Ind. Eng. Chem. Analy. Ed. 4, 248 (1932).
    [CrossRef]
  5. A. C. Hardy, J. Opt. Soc. Am. 18, 96 (1929).
    [CrossRef]

1934 (1)

1932 (1)

E. M. Shelton and R. L. Emerson, Ind. Eng. Chem. Analy. Ed. 4, 248 (1932).
[CrossRef]

1929 (1)

1928 (2)

H. J. McNicholas, Bur. Standards J. Research 1, 793 (1928).
[CrossRef]

W. D. Appel, Am. Dyestuff Reptr. 17, 49 (1928).

Appel, W. D.

W. D. Appel, Am. Dyestuff Reptr. 17, 49 (1928).

Emerson, R. L.

E. M. Shelton and R. L. Emerson, Ind. Eng. Chem. Analy. Ed. 4, 248 (1932).
[CrossRef]

Hardy, A. C.

McNicholas, H. J.

H. J. McNicholas, Bur. Standards J. Research 1, 793 (1928).
[CrossRef]

Nutting, R. D.

Shelton, E. M.

E. M. Shelton and R. L. Emerson, Ind. Eng. Chem. Analy. Ed. 4, 248 (1932).
[CrossRef]

Am. Dyestuff Reptr. (1)

W. D. Appel, Am. Dyestuff Reptr. 17, 49 (1928).

Bur. Standards J. Research (1)

H. J. McNicholas, Bur. Standards J. Research 1, 793 (1928).
[CrossRef]

Ind. Eng. Chem. Analy. Ed. (1)

E. M. Shelton and R. L. Emerson, Ind. Eng. Chem. Analy. Ed. 4, 248 (1932).
[CrossRef]

J. Opt. Soc. Am. (2)

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Figures (9)

F. 3
F. 3

Spectral reflection curves of parallel threads of green silk measured in mutually perpendicular azimuths.

F. 4
F. 4

Spectral reflection curves of green silk cloth. Upper and lower curves indicate mutually perpendicular azimuths. Center curve obtained with rotating sample.

F. 5
F. 5

Variation of reflection factor of rayon with azimuth of rotation at 400 mμ.

F. 6
F. 6

Same as Fig. 5 with photoelectric cell shielded from direct spectral reflection from rayon sample.

F. 7
F. 7

Spectral reflection curve of rayon sample used for Fig. 6. Upper and lower curves indicate mutually perpendicular azimuths. Center curve obtained with rotating sample.

Tables (6)

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Table I Wavelength = 420 mμ.

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Table II Wavelength = 500 mμ.

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Table III Wavelength = 600 mμ.

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Table IV Wavelength = 650 mμ.

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Table V Wavelength = 690 mμ.

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Table VI Wavelength = 500 mμ.

Equations (11)

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R 1 a 1 2 + R 2 a 2 2 = I 1 .
a 1 = a cos θ 1 , and a 2 = a sin θ 1 ,
I 1 = ( R 1 a 2 cos 2 θ 1 + R 2 a 2 sin 2 θ 1 ) .
I 2 = ( R 1 a 2 cos 2 θ 2 + R 2 a 2 sin 2 θ 2 ) .
1 2 ( I 1 + I 2 ) = 1 2 [ ( R 1 a 2 cos 2 θ 1 + R 2 a 2 sin 2 θ 1 ) + ( R 1 a 2 cos 2 θ 2 + R 2 a 2 sin 2 θ 2 ) ] .
θ 1 + θ 2 = 90 ° ,
cos θ 1 = sin θ 2 , and sin θ 1 = cos θ 2 .
1 2 ( I 1 + I 2 ) = 1 2 a 2 R 1 ( sin 2 θ 2 + cos 2 θ 2 ) + R 2 ( cos 2 θ 2 + sin 2 θ 2 ) .
I ave = 1 2 I ( R 1 + R 2 ) .
I ave = I ( R 1 + R 2 + + R n ) / n ,
( R 1 + R 2 + + R n ) / n = ( R 1 + R 2 ) / 2 .