Abstract

When the Sénarmont compensator is used for measuring birefringence in double refraction of flow instruments, the cross of isocline is seen to undergo a scissors-like collapsing motion as the analyzer is rotated. The position and intensity of the collapsing cross have been calculated, and are in agreement with experimental observations. From this analysis, we can directly demonstrate the end-point sensitivity of the compensator.

© 1955 Optical Society of America

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References

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  1. H. de Sénarmont, Ann. Chim. Phys. (2),  73, 337 (1840).
  2. A. von Muralt and J. T. Edsall, J. Biol. Chem. 89, 315, 351 (1930); Trans. Faraday Soc. 26, 837 (1930).
  3. C. Sadron, J. phys. radium (7),  7, 263 (1936).
    [Crossref]
  4. R. Signer and H. Gross, Z. Physik. Chem. (A),  165, 161 (1933).
  5. Edsall, Rich, and Goldstein, Rev. Sci. Inst. 23, 695, (1952).
    [Crossref]
  6. R. Cerf and H. A. Scheraga, Chem. Revs. 51, 185 (1952).
    [Crossref]
  7. The Sénarmont compensator is described briefly in Crystals and the Polarizing Microscope by N. H. Hartshorne and A. Stuart, London, 1950, Second edition p. 455. More detailed discussions are included in F. Gabler and P. Sokob, Z. f. Instrumentenk 58, 301 (1938); F. Gabler and P. Sokob, Physik. Z. 42, 319 (1941); and H. G. Jerrard, J. Opt. Soc. Am. 38, 35 (1948).
    [Crossref]
  8. Throughout this discussion, the orientation of the optic axis of the liquid as measured by the angle α is regarded as fixed, and determined by the original positions of the arms of the isocline cross before the analyzer is rotated. Thus α is an angular coordinate in the annulus. The darkened areas Q1 and Q2 move together in the annulus as the analyzer is rotated, but the values of α about the annulus remain unchanged.

1952 (2)

Edsall, Rich, and Goldstein, Rev. Sci. Inst. 23, 695, (1952).
[Crossref]

R. Cerf and H. A. Scheraga, Chem. Revs. 51, 185 (1952).
[Crossref]

1936 (1)

C. Sadron, J. phys. radium (7),  7, 263 (1936).
[Crossref]

1933 (1)

R. Signer and H. Gross, Z. Physik. Chem. (A),  165, 161 (1933).

1930 (1)

A. von Muralt and J. T. Edsall, J. Biol. Chem. 89, 315, 351 (1930); Trans. Faraday Soc. 26, 837 (1930).

1840 (1)

H. de Sénarmont, Ann. Chim. Phys. (2),  73, 337 (1840).

Cerf, R.

R. Cerf and H. A. Scheraga, Chem. Revs. 51, 185 (1952).
[Crossref]

de Sénarmont, H.

H. de Sénarmont, Ann. Chim. Phys. (2),  73, 337 (1840).

Edsall,

Edsall, Rich, and Goldstein, Rev. Sci. Inst. 23, 695, (1952).
[Crossref]

Edsall, J. T.

A. von Muralt and J. T. Edsall, J. Biol. Chem. 89, 315, 351 (1930); Trans. Faraday Soc. 26, 837 (1930).

Goldstein,

Edsall, Rich, and Goldstein, Rev. Sci. Inst. 23, 695, (1952).
[Crossref]

Gross, H.

R. Signer and H. Gross, Z. Physik. Chem. (A),  165, 161 (1933).

Hartshorne, N. H.

The Sénarmont compensator is described briefly in Crystals and the Polarizing Microscope by N. H. Hartshorne and A. Stuart, London, 1950, Second edition p. 455. More detailed discussions are included in F. Gabler and P. Sokob, Z. f. Instrumentenk 58, 301 (1938); F. Gabler and P. Sokob, Physik. Z. 42, 319 (1941); and H. G. Jerrard, J. Opt. Soc. Am. 38, 35 (1948).
[Crossref]

Rich,

Edsall, Rich, and Goldstein, Rev. Sci. Inst. 23, 695, (1952).
[Crossref]

Sadron, C.

C. Sadron, J. phys. radium (7),  7, 263 (1936).
[Crossref]

Scheraga, H. A.

R. Cerf and H. A. Scheraga, Chem. Revs. 51, 185 (1952).
[Crossref]

Signer, R.

R. Signer and H. Gross, Z. Physik. Chem. (A),  165, 161 (1933).

Stuart, A.

The Sénarmont compensator is described briefly in Crystals and the Polarizing Microscope by N. H. Hartshorne and A. Stuart, London, 1950, Second edition p. 455. More detailed discussions are included in F. Gabler and P. Sokob, Z. f. Instrumentenk 58, 301 (1938); F. Gabler and P. Sokob, Physik. Z. 42, 319 (1941); and H. G. Jerrard, J. Opt. Soc. Am. 38, 35 (1948).
[Crossref]

von Muralt, A.

A. von Muralt and J. T. Edsall, J. Biol. Chem. 89, 315, 351 (1930); Trans. Faraday Soc. 26, 837 (1930).

Ann. Chim. Phys. (2) (1)

H. de Sénarmont, Ann. Chim. Phys. (2),  73, 337 (1840).

Chem. Revs. (1)

R. Cerf and H. A. Scheraga, Chem. Revs. 51, 185 (1952).
[Crossref]

J. Biol. Chem. (1)

A. von Muralt and J. T. Edsall, J. Biol. Chem. 89, 315, 351 (1930); Trans. Faraday Soc. 26, 837 (1930).

J. phys. radium (7) (1)

C. Sadron, J. phys. radium (7),  7, 263 (1936).
[Crossref]

Rev. Sci. Inst. (1)

Edsall, Rich, and Goldstein, Rev. Sci. Inst. 23, 695, (1952).
[Crossref]

Z. Physik. Chem. (A) (1)

R. Signer and H. Gross, Z. Physik. Chem. (A),  165, 161 (1933).

Other (2)

The Sénarmont compensator is described briefly in Crystals and the Polarizing Microscope by N. H. Hartshorne and A. Stuart, London, 1950, Second edition p. 455. More detailed discussions are included in F. Gabler and P. Sokob, Z. f. Instrumentenk 58, 301 (1938); F. Gabler and P. Sokob, Physik. Z. 42, 319 (1941); and H. G. Jerrard, J. Opt. Soc. Am. 38, 35 (1948).
[Crossref]

Throughout this discussion, the orientation of the optic axis of the liquid as measured by the angle α is regarded as fixed, and determined by the original positions of the arms of the isocline cross before the analyzer is rotated. Thus α is an angular coordinate in the annulus. The darkened areas Q1 and Q2 move together in the annulus as the analyzer is rotated, but the values of α about the annulus remain unchanged.

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Figures (4)

Fig. 1
Fig. 1

Diagram of the annular field in a double refraction of flow instrument where P-P is the plane of polarization in the polarizer, A-A is the plane of polarization in the analyzer, χ is the extinction angle of the cross of isocline, and Q1, Q2 are darkened areas, arms of the cross of isocline.

Fig. 2
Fig. 2

Diagram of the optical elements and reference coordinates where P-P is the plane of polarization in the polarizer, A-A is normal to the plane of polarization in the analyzer, and O.A. is the optic axis.

Fig. 3
Fig. 3

Position of the collapsing cross of isocline as a function of the analyzer angle where α is the angular position at which scissors figure is observed in the annulus, γ is the analyzer angle, and δ is retardation.

Fig. 4
Fig. 4

The percentage intensity of occluded light at various positions of the annulus, for different retardations where α is the position in annulus and δ is retardation.

Equations (7)

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E Y = e i ω t
E Y = e i ω t cos α e - i δ / 2 E X = e i ω t sin α e + i δ / 2
E Y = e i ω t ( cos 2 α e - i δ / 2 + sin 2 α e + i δ / 2 ) cos γ E X = i e i ω t sin α cos α ( e - i δ / 2 - e + i δ / 2 ) sin γ .
I = ( E X + E Y ) ( E X * + E Y * ) = cos 2 γ + 1 2 sin 2 α sin δ sin 2 γ - sin 2 δ / 2 cos 2 γ sin 2 2 α
( I γ ) α , δ = 0
tan 2 γ = sin 2 α sin δ cos 2 2 α + sin 2 2 α cos δ
( 2 I γ 2 ) α , δ < 0