Abstract

The design and performance of an absolute deviation type of differential refractometer is described. The apparatus comprises mercury and sodium lamps, monochromatic filters, slit, differential cell, projection lens, and micrometer microscope, all accurately aligned on an optical bench. The cell is square with a thin partition separating solution and solvent, such that the angle of incidence is about 69° on the interface. The cell and its holder, in a jacketed housing, can be turned through 180° in order to interchange solvent and solution and approximately double the deviation. By ray tracing it is shown that the distance between the slit images in the eyepiece field, Δd, is accurately proportional to the difference in refractive index, Δn, of solution and solvent, and that the factor of proportionality can be evaluated from accurately measurable geometrical quantities: the cell partition angle, the virtual distance from slit to cell center, and the magnification of the system up to the field of the micrometer eyepiece. The range of the instrument is approximately 0.01 unit and the limiting sensitivity about 3 × 10−6 unit of refractive index difference. The accuracy in determination of Δn is about 0.5 percent. The instrument is useful for determination of small differences in refractive index or concentration, and for determination of refractive index increments needed in the light-scattering method of evaluating high molecular weights.

© 1951 Optical Society of America

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References

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  1. P. Debye, J. Appl. Phys. 15, 338 (1944).
    [Crossref]
  2. S. Claesson, Arkiv Kemi, Mineral. Geol. 23A, No. 1, 1 (1946).
  3. H. J. Dutton, J. Phys. Chem. 48, 179 (1944).
    [Crossref]
  4. D. Zaukelies and A. A. Frost, Anal. Chem. 21, 743 (1949).
    [Crossref]
  5. Thomas, O’Konski, and Hurd, Anal. Chem. 22, 1221 (1950).
    [Crossref]
  6. D. Rau and W. E. Roseveare, Ind. Eng. Chem., Anal. Ed.  8, 72 (1936).
  7. R. Kocholaty, Food Research 15, 347 (1950).
    [Crossref]
  8. L. G. Longsworth, Ind. Eng. Chem., Anal. Ed.  18, 219 (1946).
  9. G. Kegeles, J. Am. Chem. Soc. 69, 1302 (1947).
    [Crossref] [PubMed]
  10. A. Weissberger, ed., Physical Methods of Organic Chemistry (Interscience Publishers, Inc., New York, 1949), second edition, Vol. I, Chapter XX ( Bauer and Fajans).
  11. H. Kessler, Handbuch der Physik 18, 668–679 (1927).
  12. P. P. Debye, J. Appl. Phys. 17, 392 (1946).
    [Crossref]
  13. Hadow, Sheffer, and Hyde, Can. J. Research 27B, 791 (1949).
    [Crossref]
  14. R. F. Stamm, J. Opt. Soc. Am. 40, 788 (L) (1950).
    [Crossref]
  15. B. A. Brice and R. Speiser, J. Opt. Soc. Am. 36, 363A (1946).
  16. Brice, Halwer, and Speiser, J. Opt. Soc. Am. 40, 768 (1950).
    [Crossref]
  17. A. Kruis, Z. physik Chem. 34B, 13 (1936).
  18. F. J. Bates and Associates, Natl. Bur. Standards (U. S.), Circ. C440 (May1, 1942). See also C. A. Browne and F. W. Zerban, Physical and Chemical Methods of Sugar Analysis (John Wiley and Sons, Inc., New York, 1941), third edition, Table 6.
  19. L. W. Tilton, J. Research Natl. Bur. Standards 17, 639 (1936).
    [Crossref]
  20. L. W. Tilton and J. K. Taylor, J. Research Natl. Bur. Standards 20, 419 (1938).
    [Crossref]

1950 (4)

Thomas, O’Konski, and Hurd, Anal. Chem. 22, 1221 (1950).
[Crossref]

R. Kocholaty, Food Research 15, 347 (1950).
[Crossref]

R. F. Stamm, J. Opt. Soc. Am. 40, 788 (L) (1950).
[Crossref]

Brice, Halwer, and Speiser, J. Opt. Soc. Am. 40, 768 (1950).
[Crossref]

1949 (2)

Hadow, Sheffer, and Hyde, Can. J. Research 27B, 791 (1949).
[Crossref]

D. Zaukelies and A. A. Frost, Anal. Chem. 21, 743 (1949).
[Crossref]

1947 (1)

G. Kegeles, J. Am. Chem. Soc. 69, 1302 (1947).
[Crossref] [PubMed]

1946 (4)

P. P. Debye, J. Appl. Phys. 17, 392 (1946).
[Crossref]

B. A. Brice and R. Speiser, J. Opt. Soc. Am. 36, 363A (1946).

S. Claesson, Arkiv Kemi, Mineral. Geol. 23A, No. 1, 1 (1946).

L. G. Longsworth, Ind. Eng. Chem., Anal. Ed.  18, 219 (1946).

1944 (2)

H. J. Dutton, J. Phys. Chem. 48, 179 (1944).
[Crossref]

P. Debye, J. Appl. Phys. 15, 338 (1944).
[Crossref]

1942 (1)

F. J. Bates and Associates, Natl. Bur. Standards (U. S.), Circ. C440 (May1, 1942). See also C. A. Browne and F. W. Zerban, Physical and Chemical Methods of Sugar Analysis (John Wiley and Sons, Inc., New York, 1941), third edition, Table 6.

1938 (1)

L. W. Tilton and J. K. Taylor, J. Research Natl. Bur. Standards 20, 419 (1938).
[Crossref]

1936 (3)

L. W. Tilton, J. Research Natl. Bur. Standards 17, 639 (1936).
[Crossref]

D. Rau and W. E. Roseveare, Ind. Eng. Chem., Anal. Ed.  8, 72 (1936).

A. Kruis, Z. physik Chem. 34B, 13 (1936).

1927 (1)

H. Kessler, Handbuch der Physik 18, 668–679 (1927).

Bates, F. J.

F. J. Bates and Associates, Natl. Bur. Standards (U. S.), Circ. C440 (May1, 1942). See also C. A. Browne and F. W. Zerban, Physical and Chemical Methods of Sugar Analysis (John Wiley and Sons, Inc., New York, 1941), third edition, Table 6.

Bauer,

A. Weissberger, ed., Physical Methods of Organic Chemistry (Interscience Publishers, Inc., New York, 1949), second edition, Vol. I, Chapter XX ( Bauer and Fajans).

Brice,

Brice, B. A.

B. A. Brice and R. Speiser, J. Opt. Soc. Am. 36, 363A (1946).

Claesson, S.

S. Claesson, Arkiv Kemi, Mineral. Geol. 23A, No. 1, 1 (1946).

Debye, P.

P. Debye, J. Appl. Phys. 15, 338 (1944).
[Crossref]

Debye, P. P.

P. P. Debye, J. Appl. Phys. 17, 392 (1946).
[Crossref]

Dutton, H. J.

H. J. Dutton, J. Phys. Chem. 48, 179 (1944).
[Crossref]

Fajans,

A. Weissberger, ed., Physical Methods of Organic Chemistry (Interscience Publishers, Inc., New York, 1949), second edition, Vol. I, Chapter XX ( Bauer and Fajans).

Frost, A. A.

D. Zaukelies and A. A. Frost, Anal. Chem. 21, 743 (1949).
[Crossref]

Hadow,

Hadow, Sheffer, and Hyde, Can. J. Research 27B, 791 (1949).
[Crossref]

Halwer,

Hurd,

Thomas, O’Konski, and Hurd, Anal. Chem. 22, 1221 (1950).
[Crossref]

Hyde,

Hadow, Sheffer, and Hyde, Can. J. Research 27B, 791 (1949).
[Crossref]

Kegeles, G.

G. Kegeles, J. Am. Chem. Soc. 69, 1302 (1947).
[Crossref] [PubMed]

Kessler, H.

H. Kessler, Handbuch der Physik 18, 668–679 (1927).

Kocholaty, R.

R. Kocholaty, Food Research 15, 347 (1950).
[Crossref]

Kruis, A.

A. Kruis, Z. physik Chem. 34B, 13 (1936).

Longsworth, L. G.

L. G. Longsworth, Ind. Eng. Chem., Anal. Ed.  18, 219 (1946).

O’Konski,

Thomas, O’Konski, and Hurd, Anal. Chem. 22, 1221 (1950).
[Crossref]

Rau, D.

D. Rau and W. E. Roseveare, Ind. Eng. Chem., Anal. Ed.  8, 72 (1936).

Roseveare, W. E.

D. Rau and W. E. Roseveare, Ind. Eng. Chem., Anal. Ed.  8, 72 (1936).

Sheffer,

Hadow, Sheffer, and Hyde, Can. J. Research 27B, 791 (1949).
[Crossref]

Speiser,

Speiser, R.

B. A. Brice and R. Speiser, J. Opt. Soc. Am. 36, 363A (1946).

Stamm, R. F.

R. F. Stamm, J. Opt. Soc. Am. 40, 788 (L) (1950).
[Crossref]

Taylor, J. K.

L. W. Tilton and J. K. Taylor, J. Research Natl. Bur. Standards 20, 419 (1938).
[Crossref]

Thomas,

Thomas, O’Konski, and Hurd, Anal. Chem. 22, 1221 (1950).
[Crossref]

Tilton, L. W.

L. W. Tilton and J. K. Taylor, J. Research Natl. Bur. Standards 20, 419 (1938).
[Crossref]

L. W. Tilton, J. Research Natl. Bur. Standards 17, 639 (1936).
[Crossref]

Zaukelies, D.

D. Zaukelies and A. A. Frost, Anal. Chem. 21, 743 (1949).
[Crossref]

Anal. Chem. (2)

D. Zaukelies and A. A. Frost, Anal. Chem. 21, 743 (1949).
[Crossref]

Thomas, O’Konski, and Hurd, Anal. Chem. 22, 1221 (1950).
[Crossref]

Arkiv Kemi, Mineral. Geol. (1)

S. Claesson, Arkiv Kemi, Mineral. Geol. 23A, No. 1, 1 (1946).

Can. J. Research (1)

Hadow, Sheffer, and Hyde, Can. J. Research 27B, 791 (1949).
[Crossref]

Food Research (1)

R. Kocholaty, Food Research 15, 347 (1950).
[Crossref]

Handbuch der Physik (1)

H. Kessler, Handbuch der Physik 18, 668–679 (1927).

Ind. Eng. Chem. (2)

L. G. Longsworth, Ind. Eng. Chem., Anal. Ed.  18, 219 (1946).

D. Rau and W. E. Roseveare, Ind. Eng. Chem., Anal. Ed.  8, 72 (1936).

J. Am. Chem. Soc. (1)

G. Kegeles, J. Am. Chem. Soc. 69, 1302 (1947).
[Crossref] [PubMed]

J. Appl. Phys. (2)

P. P. Debye, J. Appl. Phys. 17, 392 (1946).
[Crossref]

P. Debye, J. Appl. Phys. 15, 338 (1944).
[Crossref]

J. Opt. Soc. Am. (3)

R. F. Stamm, J. Opt. Soc. Am. 40, 788 (L) (1950).
[Crossref]

B. A. Brice and R. Speiser, J. Opt. Soc. Am. 36, 363A (1946).

Brice, Halwer, and Speiser, J. Opt. Soc. Am. 40, 768 (1950).
[Crossref]

J. Phys. Chem. (1)

H. J. Dutton, J. Phys. Chem. 48, 179 (1944).
[Crossref]

J. Research Natl. Bur. Standards (2)

L. W. Tilton, J. Research Natl. Bur. Standards 17, 639 (1936).
[Crossref]

L. W. Tilton and J. K. Taylor, J. Research Natl. Bur. Standards 20, 419 (1938).
[Crossref]

Natl. Bur. Standards (U. S.), Circ. C440 (1)

F. J. Bates and Associates, Natl. Bur. Standards (U. S.), Circ. C440 (May1, 1942). See also C. A. Browne and F. W. Zerban, Physical and Chemical Methods of Sugar Analysis (John Wiley and Sons, Inc., New York, 1941), third edition, Table 6.

Z. physik Chem. (1)

A. Kruis, Z. physik Chem. 34B, 13 (1936).

Other (1)

A. Weissberger, ed., Physical Methods of Organic Chemistry (Interscience Publishers, Inc., New York, 1949), second edition, Vol. I, Chapter XX ( Bauer and Fajans).

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Figures (3)

Fig. 1
Fig. 1

Diagrammatic sketch of optical system of differential refractometer. Hg, mercury lamp in housing; F, monochromatic filters; R, semi-transparent mirror for viewing sodium lamp, Na; S, spectrometer slit; C, differential cell; H, jacketed cell housing; P, projector lens; M, micrometer microscope.

Fig. 2
Fig. 2

Photograph of differential cell in jacketed housing. The spectrometer slit and optical bench are partly shown.

Fig. 3
Fig. 3

Path of central ray OABCDEF through differential cell with thin partition (diagrammatic plan). The final angle of deviation is r, and the virtual image of the slit is at H (with deviations exaggerated); n0, n, and nw are the refractive indices of solvent, solution, and glass windows, respectively.

Tables (4)

Tables Icon

Table I Calibration of differential refractometer.

Tables Icon

Table II Comparison of results for the difference in refractive index between KCl solutions and distilled water at 25.0°C and for wavelength 589 mμ.

Tables Icon

Table III Comparison of difference in refractive index between sucrose solutions and distilled water, as determined by the differential refractometer and as calculated from reference 18, for 589 mμ and 20°C.

Tables Icon

Table IV Specific refractive increments for various solute-solvent systems determined with the differential refractometer. Units of concentration for Δn/c are grams per ml of solution.

Equations (23)

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Δ d = ( d 1 - d 2 ) - ( d 01 - d 02 ) .
Δ n = k Δ d ,
n 0 sin i = n sin r 1 ,
n sin ( i - r 1 ) = n w sin r 2 = sin r .
n ( i - r 1 ) = r .
n 0 sin i = n sin ( i - r / n ) .
n - n 0 = r cot i + r 2 / 2 n .
n - n 0 = r cot i - r 2 / 2 n 0 .
n - n 0 = 1 2 ( r + r ) cot i .
r = S H / S G = ( d 0 - d 2 ) / m S G ,
S G = O G - O S = a + t + b / 2 + C G - O S .
C G = C K - G K = b / 2 + t - K E / r .
K E = J D + L E = ( b / 2 ) ( i - r 1 ) + r 2 t .
K E = ( b / 2 ) ( r / n ) + t r / n w .
C G = ( b / 2 ) ( n - 1 ) / n + t ( n w - 1 ) / n w .
O S = ( b / 2 ) ( n 0 - 1 ) / n 0 + ( b / 2 ) ( n - 1 ) / n + 2 t ( n w - 1 ) / n w .
S G = a + b / 2 n 0 + t / n w ,
r = ( d 0 - d 2 ) / m ( a + b / 2 n 0 + t / n w ) .
r = ( d 1 - d 0 ) / m ( a + b / 2 n + t / n w ) ,
r + r = ( d 1 - d 2 ) / m 0 ( a + b / 2 n 0 + t / n w ) .
n - n 0 = ( d 1 - d 2 ) ( cot i ) / 2 m 0 ( a + b / 2 n 0 + t / n w ) ,
Δ n = k Δ d ,
k = ( cot i ) / 2 m 0 ( a + b / 2 n 0 + t / n w ) .