Abstract

Extinction directions in a medium M may be found by using a polarizer P, a Nakamura half-shade H, and an analyzer A. These components are set up with P and A crossed and so that monochromatic light passes in turn through P, M, H, and A to enter a microscope focused on the dividing line of H. The extinction directions are found by rotating M until the field of view is of uniform brightness: they coincide then with the vibration directions of P and A. This method is considered in detail, and it is shown on theoretical grounds that, for media having a phase difference less than π/2, increased sensitivity results when a quarter-wave plate Q is inserted, in zero azimuth with respect to the vibration direction of P, between M and H. The calculated increase for very small phase differences is considerable: experiment confirms this. A comparison is made with a method in which H is a half-shade of the Bravais type and Q is omitted. The present arrangement serves also as a sensitive compensator for the measurement of optical phase differences and it is, therefore, particularly suitable for measurements, such as occur in flow birefringence studies, where both extinction angles and the magnitude of the birefringence are required. This application is discussed.

© 1956 Optical Society of America

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References

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  1. See review by J. T. Edsall, Advances in Colloid Science (Interscience Publishers, Inc., New York, 1942), Vol. 1, p. 269.
  2. S. Nakamura, Zentr. Mineral. Geol. u. Paläontol. 6, 267 (1905).
  3. H. G. Jerrard, J. Opt. Soc. Am. 44, 289 (1954).
    [CrossRef]
  4. H. G. Jerrard, J. Opt. Soc. Am. 38, 35 (1948).
    [CrossRef]
  5. H. G. Jerrard, J. Opt. Soc. Am. 44, 292 (1954).
  6. C. Zakrzewski, Bull. intern. acad. sci. Cracovie 1, 50 (1904).
  7. R. Cerf, Rev. opt. 29, 200 (1950).
  8. C. Zakrzewski and C. Kraft, Bull. intern. acad. sci. Cracovie 2, 506 (1905).
  9. L. B. Tuckerman, Univ. Nebraska Studies 9,(2) 157 (1909).

1954 (2)

H. G. Jerrard, J. Opt. Soc. Am. 44, 292 (1954).

H. G. Jerrard, J. Opt. Soc. Am. 44, 289 (1954).
[CrossRef]

1950 (1)

R. Cerf, Rev. opt. 29, 200 (1950).

1948 (1)

1909 (1)

L. B. Tuckerman, Univ. Nebraska Studies 9,(2) 157 (1909).

1905 (2)

S. Nakamura, Zentr. Mineral. Geol. u. Paläontol. 6, 267 (1905).

C. Zakrzewski and C. Kraft, Bull. intern. acad. sci. Cracovie 2, 506 (1905).

1904 (1)

C. Zakrzewski, Bull. intern. acad. sci. Cracovie 1, 50 (1904).

Cerf, R.

R. Cerf, Rev. opt. 29, 200 (1950).

Edsall, J. T.

See review by J. T. Edsall, Advances in Colloid Science (Interscience Publishers, Inc., New York, 1942), Vol. 1, p. 269.

Jerrard, H. G.

Kraft, C.

C. Zakrzewski and C. Kraft, Bull. intern. acad. sci. Cracovie 2, 506 (1905).

Nakamura, S.

S. Nakamura, Zentr. Mineral. Geol. u. Paläontol. 6, 267 (1905).

Tuckerman, L. B.

L. B. Tuckerman, Univ. Nebraska Studies 9,(2) 157 (1909).

Zakrzewski, C.

C. Zakrzewski and C. Kraft, Bull. intern. acad. sci. Cracovie 2, 506 (1905).

C. Zakrzewski, Bull. intern. acad. sci. Cracovie 1, 50 (1904).

Bull. intern. acad. sci. Cracovie (2)

C. Zakrzewski, Bull. intern. acad. sci. Cracovie 1, 50 (1904).

C. Zakrzewski and C. Kraft, Bull. intern. acad. sci. Cracovie 2, 506 (1905).

J. Opt. Soc. Am. (3)

Rev. opt. (1)

R. Cerf, Rev. opt. 29, 200 (1950).

Univ. Nebraska Studies (1)

L. B. Tuckerman, Univ. Nebraska Studies 9,(2) 157 (1909).

Zentr. Mineral. Geol. u. Paläontol. (1)

S. Nakamura, Zentr. Mineral. Geol. u. Paläontol. 6, 267 (1905).

Other (1)

See review by J. T. Edsall, Advances in Colloid Science (Interscience Publishers, Inc., New York, 1942), Vol. 1, p. 269.

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Figures (2)

Fig. 1
Fig. 1

The parameters. P, polarizer; A, analyzer; M, doubly refracting medium; H, half-shadow plate; T, observation microscope; OP and OA are the vibration directions of the polarizer and analyzer, respectively; OX and OY are the fast and slow vibration directions of the medium; ν1 and φ1 are the azimuths measured from OX of OP and the major axis OE of the elliptical vibration leaving M respectively.

Fig. 2
Fig. 2

Variation of half-shadow sensitivity with phase difference. Curves 1 and 2 give the sensitivities with and without a λ/4 plate respectively. The ordinates are S/4 cotρ where S is the sensitivity and ρ the rotation of the Nakamura plate. Curve 3 shows the ratio of the sensitivities (SN/S).

Tables (2)

Tables Icon

Table I Experimental results for location of extinction directions in medium giving different phase differences (normal conditions of observation: 20 readings).

Tables Icon

Table II Half-shadow sensitivities and intensities of field of view for different Nakamura plates (N.P.), and different Bravais plates (B.P.) in two positions (β).a

Equations (14)

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sin 2 1 = ± sin 2 ν 1 sin δ 1 ,
tan 2 φ 1 = tan 2 ν 1 cos δ 1 .
J 1 = sin 2 ρ - sin 2 ν 1 sin 2 ( ρ - ν 1 ) sin 2 δ 1 / 2 ,
J 2 = sin 2 ρ + sin 2 ν 1 sin 2 ( ρ + ν 1 ) sin 2 δ 1 / 2.
J 2 - J 1 = sin 2 ρ sin 4 ν 1 sin 2 δ 1 / 2.
S = [ ( J 2 p - J 1 p / ) J ] p 0 .
S = 8 cot ρ sin 2 δ 1 / 2 = 4 cot ρ [ 1 - cos δ 1 ] ,
J 1 = sin 2 ρ - sin 2 ν 1 sin 2 ( ρ - ν 1 ) × sin 2 δ 1 / 2 - sin 2 ν 1 sin 2 ρ sin δ 1 / 2 × ( cos δ 1 / 2 - cos 2 ν 1 sin δ 1 / 2 ) , J 2 = sin 2 ρ + sin 2 ν 1 sin 2 ( ρ + ν 1 ) × sin 2 δ 1 / 2 + sin 2 ν 1 sin 2 ρ sin δ 1 / 2 × ( cos δ 1 / 2 - cos 2 ν 1 sin δ 1 / 2 ) .
J 2 - J 1 = sin 2 ρ sin 2 ν 1 sin δ 1 .
J 1 = J 2 = sin 2 ρ .
S N = 4 cot ρ sin δ 1 ,
J 1 - J 2 = sin 2 ν 1 sin 2 β sin δ 1 sin η ,
J = sin 2 2 β sin 2 η / 2 ,
S B = 4 cot η / 2 sin δ 1 / sin 2 β ,