Abstract

Provided that the difficulties associated with the high temperature coefficient of refractive index of the liquid component can be overcome, there appear to be certain advantages in the use of compound liquid-glass prisms (Zenger or Wernicke type), in Raman spectrographs. In particular, the curvature of the slit image is negligible, an important factor if photoelectric recording is used. The theoretical equations for dispersion, resolving power and image curvature for such systems have been derived. A small Littrow-mounted Zenger prism has been constructed, and a solution of mercuric bromide in aqueous barium bromide solution chosen as the liquid component after studying its optical constants. Without using elaborate thermostatic control, satisfactory spectrograms of the iron arc have been obtained. The practical resolution in the relatively crude experiments (1500 in the wavelength range λ=4200–5000A) was limited by the slit width used, and the reciprocal dispersion in the neighborhood of λ=4400A was found to be 25A/mm. No appreciable curvature of the slit image was observed with a slit height of 2.5 cm.

© 1952 Optical Society of America

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References

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  1. G. R. Harrison, Rev. Sci. Instr. 5, 149 (1934).
    [Crossref]
  2. K. W. Zenger, Z. f. Instrkde. 1, 263 (1881).
  3. W. Wernicke, Z. f. Instrkde. 1, 355 (1881).
  4. R. A. Sawyer, Experimental Spectroscopy (Prentice-Hall, Inc., New York, 1944), p. 73.
  5. E. C. C. Baly, Spectroscopy (Longmans, Green and Company, New York, 1924), third edition, Vol. I, p. 66; F. P. Pickering, Phil. Mag. (4),  36, 39 (1868); F. L. O. Wadsworth, Astrophys. J. 2, 264 (1895).
    [Crossref]
  6. W. E. Forsythe, Measurement of Radiant Energy (McGraw-Hill Book Company, Inc., New York, 1937), p. 176. H. Kayser, Handbuch der Spectroscopie, Vol. 1 (Hirzel, 1900), p. 319.
  7. Rayleigh, Scientific Papers (Cambridge University Press, London, 1900) Vol. 2, p. 412; Scientific Papers Vol. 3, p. 105.
  8. Rayleigh, Scientific Papers (Cambridge University Press, London, 1899) Vol. 1, p. 425.
  9. G. G. Stokes, Proc. Roy. Soc. (London) 22, 310 (1874).
  10. Catalog E 25 (Adam Hilger, Ltd., London, July, 1937) (now Hilger & Watts).
  11. J. Duclaux and G. Ahier, Rev. d’Optique 17, 417 (1938). (See also P. Jeantet and J. Duclaux, Rev. d’Optique 14, 345 (1935).
  12. J. A. Brashear, English Mechanic 31, 237 (1890). J. Strong, Modern Physical Laboratory Practice (Prentice-Hall, Inc., New York, and Blackie and Sons, Ltd., London, 1938), p. 154.
  13. See reference 4, p. 59.
  14. International Critical TablesII, 106 (McGraw-Hill Book Company, Inc., New York, 1926).

1938 (1)

J. Duclaux and G. Ahier, Rev. d’Optique 17, 417 (1938). (See also P. Jeantet and J. Duclaux, Rev. d’Optique 14, 345 (1935).

1934 (1)

G. R. Harrison, Rev. Sci. Instr. 5, 149 (1934).
[Crossref]

1890 (1)

J. A. Brashear, English Mechanic 31, 237 (1890). J. Strong, Modern Physical Laboratory Practice (Prentice-Hall, Inc., New York, and Blackie and Sons, Ltd., London, 1938), p. 154.

1881 (2)

K. W. Zenger, Z. f. Instrkde. 1, 263 (1881).

W. Wernicke, Z. f. Instrkde. 1, 355 (1881).

1874 (1)

G. G. Stokes, Proc. Roy. Soc. (London) 22, 310 (1874).

Ahier, G.

J. Duclaux and G. Ahier, Rev. d’Optique 17, 417 (1938). (See also P. Jeantet and J. Duclaux, Rev. d’Optique 14, 345 (1935).

Baly, E. C. C.

E. C. C. Baly, Spectroscopy (Longmans, Green and Company, New York, 1924), third edition, Vol. I, p. 66; F. P. Pickering, Phil. Mag. (4),  36, 39 (1868); F. L. O. Wadsworth, Astrophys. J. 2, 264 (1895).
[Crossref]

Brashear, J. A.

J. A. Brashear, English Mechanic 31, 237 (1890). J. Strong, Modern Physical Laboratory Practice (Prentice-Hall, Inc., New York, and Blackie and Sons, Ltd., London, 1938), p. 154.

Duclaux, J.

J. Duclaux and G. Ahier, Rev. d’Optique 17, 417 (1938). (See also P. Jeantet and J. Duclaux, Rev. d’Optique 14, 345 (1935).

Forsythe, W. E.

W. E. Forsythe, Measurement of Radiant Energy (McGraw-Hill Book Company, Inc., New York, 1937), p. 176. H. Kayser, Handbuch der Spectroscopie, Vol. 1 (Hirzel, 1900), p. 319.

Harrison, G. R.

G. R. Harrison, Rev. Sci. Instr. 5, 149 (1934).
[Crossref]

Rayleigh,

Rayleigh, Scientific Papers (Cambridge University Press, London, 1900) Vol. 2, p. 412; Scientific Papers Vol. 3, p. 105.

Rayleigh, Scientific Papers (Cambridge University Press, London, 1899) Vol. 1, p. 425.

Sawyer, R. A.

R. A. Sawyer, Experimental Spectroscopy (Prentice-Hall, Inc., New York, 1944), p. 73.

Stokes, G. G.

G. G. Stokes, Proc. Roy. Soc. (London) 22, 310 (1874).

Wernicke, W.

W. Wernicke, Z. f. Instrkde. 1, 355 (1881).

Zenger, K. W.

K. W. Zenger, Z. f. Instrkde. 1, 263 (1881).

English Mechanic (1)

J. A. Brashear, English Mechanic 31, 237 (1890). J. Strong, Modern Physical Laboratory Practice (Prentice-Hall, Inc., New York, and Blackie and Sons, Ltd., London, 1938), p. 154.

Proc. Roy. Soc. (London) (1)

G. G. Stokes, Proc. Roy. Soc. (London) 22, 310 (1874).

Rev. d’Optique (1)

J. Duclaux and G. Ahier, Rev. d’Optique 17, 417 (1938). (See also P. Jeantet and J. Duclaux, Rev. d’Optique 14, 345 (1935).

Rev. Sci. Instr. (1)

G. R. Harrison, Rev. Sci. Instr. 5, 149 (1934).
[Crossref]

Z. f. Instrkde. (2)

K. W. Zenger, Z. f. Instrkde. 1, 263 (1881).

W. Wernicke, Z. f. Instrkde. 1, 355 (1881).

Other (8)

R. A. Sawyer, Experimental Spectroscopy (Prentice-Hall, Inc., New York, 1944), p. 73.

E. C. C. Baly, Spectroscopy (Longmans, Green and Company, New York, 1924), third edition, Vol. I, p. 66; F. P. Pickering, Phil. Mag. (4),  36, 39 (1868); F. L. O. Wadsworth, Astrophys. J. 2, 264 (1895).
[Crossref]

W. E. Forsythe, Measurement of Radiant Energy (McGraw-Hill Book Company, Inc., New York, 1937), p. 176. H. Kayser, Handbuch der Spectroscopie, Vol. 1 (Hirzel, 1900), p. 319.

Rayleigh, Scientific Papers (Cambridge University Press, London, 1900) Vol. 2, p. 412; Scientific Papers Vol. 3, p. 105.

Rayleigh, Scientific Papers (Cambridge University Press, London, 1899) Vol. 1, p. 425.

Catalog E 25 (Adam Hilger, Ltd., London, July, 1937) (now Hilger & Watts).

See reference 4, p. 59.

International Critical TablesII, 106 (McGraw-Hill Book Company, Inc., New York, 1926).

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Figures (9)

Fig. 1
Fig. 1

Compound liquid-glass prisms. (a) Zenger prism. (b) Wernicke prism.

Fig. 2
Fig. 2

Path of a light ray through a compound liquid-glass prism of the Wernicke type.

Fig. 3
Fig. 3

Principal sections of Wernicke prism.

Fig. 4
Fig. 4

Schematic relationship of curvature of slit image and wavelength for Wernicke prism. λ0 is the wavelength at which the refractive indices of both parts are matched (δn=0). At other wavelengths δn is either positive or negative and the slit image will be curved accordingly.

Fig. 5
Fig. 5

Absorption curves of mercuric bromide in barium bromide solution, relative to water. —×— Solution used in the Littrow mounted Zenger prism. —⊙—Solution saturated with respect to both salts at room temperature (18°C).

Fig. 6
Fig. 6

The relation between the refractive index for λ=5460A, and the difference δn in the refractive indices measured at λ=4360A and λ=5790A, for solutions of mercuric bromide in barium bromide. (For water at 21°C n5460=1.3344, δn=0.0069.) —×— Solution saturated with respect to both salts. —◬— Saturated solution diluted with saturated barium bromide solution. —⊙— Saturated solution diluted with water.

Fig. 7
Fig. 7

Plan and front elevation of the Littrow mounted Zenger prism used. (Not to scale. Dotted line represents outline of block in which prism was mounted.) (a) Plan. (b) Elevation.

Fig. 8
Fig. 8

Enlargement of portion of iron arc spectrum. Ilford Press Ortho Series II plate. Slit 0.125 mm. Focal length of 91 cm. (a) 6-sec exposure. (b) 2-sec exposure.

Fig. 9
Fig. 9

The variation of reciprocal dispersion (A/mm) with wavelength for the experimental Zenger prism. —×— Measured from iron arc spectrum (Fig. 8). —⊙— Calculated from Eq. (13).

Tables (3)

Tables Icon

Table I Optical properties of some liquids which have been proposed for use in liquid prisms.

Tables Icon

Table II Optical constants of components used in Littrow mounted Zenger prism.

Tables Icon

Table III Comparison of performance of Zenger prism with orthodox arrangements employing a single glass prism of comparable size.

Equations (32)

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sin r = sin ( β - ϕ ) / n S ,
sin r = n S sin ( α + β - r ) / n L ,
sin r = n L sin ( 2 α - r ) / n S ,
sin ( β - ϕ ) = n S sin ( α + β - r ) .
sin ( β - ϕ ) = sin ( α + β ) ( n S 2 - n L 2 sin 2 ( 2 α - r ) ) - n L cos ( α + β ) sin ( 2 α - r ) .
n L = n S + δ n
1 n S sin ( β - ϕ ) = - sin ( α - β - r ) - δ n n S tan ( 2 α - r ) cos ( α - β - r ) .
sin ( α - β - r ) = sin ( r - 2 β ) + δ n n S cos ( r - 2 β ) tan ( α + β - r ) , tan ( 2 α - r ) = tan ( α - β + r ) + δ n n S tan ( α + β - r ) cos 2 ( α - β - r ) , cos ( α - β - r ) = cos ( r - 2 β ) - δ n n S sin ( r - 2 β ) tan ( α + β - r ) .
1 n S sin ( β - ϕ ) = - sin ( r - 2 β ) - δ n n S sin 2 α cos 2 α + cos 2 ( β - r ) .
sin ( β - ϕ ) = - sin ( β - ϕ ) cos 2 β + { n S 2 - sin 2 ( β - ϕ ) } sin 2 β - δ n n S { sin ( β - ϕ ) sin 2 β + { n S 2 - sin 2 ( β - ϕ ) } cos 2 β } × n S 2 sin 2 α { n S 2 cos 2 α - [ sin ( β - ϕ ) cos 2 β - { n S 2 - sin 2 ( β - ϕ ) } sin 2 β ] 2 } .
- sin ϕ = sin ϕ - δ n n S sin 2 α ( n S 2 - sin 2 ϕ ) ( n S 2 cos 2 α - sin 2 ϕ ) .
sin ϕ = δ n sin 2 α / cos 2 α = 2 tan α - δ n δ λ δ λ .
sin ( β - ϕ ) = - ( β - ϕ ) cos 2 β + n S sin 2 β - δ n n S { ( β - ϕ ) sin 2 β + n S cos 2 β } sin 2 α [ n S 2 cos 2 α - { ( β - ϕ ) cos 2 β - n S sin 2 β } 2 ] .
sin ( β - ϕ ) = n S sin 2 β - δ n sin 2 α cos 2 β cos 2 α - sin 2 2 β .
sin ( β - ϕ ) = 2 n S β - δ n sin 2 α / cos 2 α .
( ϕ / λ ) = 2 tan α ( n / λ ) .
2 X C + 2 n L · l = 2 Y D + 2 n S · l .
X C + 2 ( n L + δ n L ) l + C Z = 2 Y D + 2 ( n S + δ n S ) l .
p = C D δ θ = Z X = C X - C Z , = 2 l · δ ( n S ~ n L ) .
δ θ = λ / a ,
λ = 2 l ( / λ ) ( n S ~ n L ) δ λ , λ / δ λ = 2 l ( / λ ) ( n S ~ n L ) = R .
n S = sin θ sin θ ;             n L n S = sin θ sin θ ;             n S n L = sin θ sin θ ;             1 n S = sin θ sin θ iv .
sin θ = sin θ / n S ;             sin θ = sin θ / n L ; sin θ = sin θ / n S ;             sin θ iv = sin θ .
n S cos θ / cos θ ;             n L cos θ / cos θ ; n S cos θ / cos θ ;             n S cos θ / cos θ .
μ S = n S cos θ / cos θ ;             μ L = n L cos θ / cos θ ;             δ μ = μ L - μ S ,
δ μ = { n L cos θ - n S cos θ } / cos θ = { n S ( cos θ - cos θ ) + δ n cos θ } / cos θ = n S ( θ 2 - θ 2 ) / ( 2 cos θ ) + 2 δ n ( 1 - 1 2 θ 2 ) / cos θ .
θ = sin θ = sin θ / n S = θ / n S ,
θ = sin θ ( 1 - δ n n S ) / n S .
δ μ = δ n cos θ ( 1 + sin 2 θ 2 n S 2 ) = δ n ( 1 + θ 2 2 ( n S 2 + 1 n S 2 ) ) .
- sin ϕ = 2 δ n { 1 + θ 2 2 ( n S 2 + 1 n S 2 ) } tan α .
ρ = f 2 δ n n S 2 ( n S 2 + 1 ) | tan 2 α .
λ 0 = 2034.57 A ,             C = 146.2336 ,             n 0 = 1.61738 ;