Light Scattering Functions for Spherical Particles with m = 165 (005) 185
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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA Light Scattering Functions for Spherical Particles with m=1.65 (0.05) 1.85 E. J. MEEHAN AND Z Z. HUGUS Sc/tool of Cheinistry, University of Minnesota, Minneapolis, Minnesota (Received September 13, 1960) Mie theory calculations are presented for scattering coefficient and forward scattering by spherical particles with in= 1.65 (0.05) 1.85 and a up to 6.0. IN connection with certain light-scattering studies, Mie theory calculations were required for values of the refractive index ratio in in the range 1.65-1.85. A few values of the scattering coefficient K and forward scattering i(0) have been obtained previously by hand calculation for ,= 1.75 and 15 values of a up to 3.6.2 The present calculations for in= 1.65 (0.05) 1.85 and 48 values of ae up to 6.0 were carried out on a Univac Scientific (1103) computer. The computer program was arranged to terminate when the absolute value of the largest of the four quantities R(An), I(An), R(Pn), and I(Pn) became smaller than 5X10-. Values of K and i(0) were obtained to seven figures, and all the values have been uniformly rounded to five figures in Table I. From the results it appears that the spacing of m(0.05) is close enough to permit reliable interpo- lation to intermediate m up to an a of about 3.0. All the hand-calculated values of K reported previously for i= 1.75 have been confirmed, with the exception of that for a= 1.8, which was in error by -1.9%. While these calculations were under way some values of K for in= 1.831 were published in graphical form. 3 It appeared of interest to extend these calculations, and accordingly some values of K and i(0) for m= 1.831 are included in Table I. TAnLE I. Values of K and i(0). inI =1.65 . I =1.70 in =1.75 in =1.80 in =1.831 n =1.85 a K i (O) K it (0) K i () K i (0) K it (0) K it (0) 0.5 0.023022 0.0024303 0.026072 0.0027585 0.029209 0.0030975 0.032415 0.0034460 0.034432 0.0036661 0.035677 0.0038024 0.6 0.048231 0.0077004 0.054811 0.0087778 0.061612 0.0098990 0.068602 0.011060 0.073017 0.011797 0.075749 0.012255 0.7 0.089905 0.020672 0.10255 0.023675 0.11570 0.026825 0.12929 0.030111 0.13791 0.032213 0.14326 0.033524 0.8 0.15312 0.049020 0.17530 0.056411 0.19848 0.064226 0.22258 0.072450 0.23795 0.077748 0.24751 0.081069 0.9 0.24190 0.10533 0.27781 0.12177 0.31555 0.13931 0.35498 0.15792 0.38022 0.17001 0.39598 0.17763 1.0 0.35774 0.20859 0.41183 0.24220 0.46891 0.27837 0.52887 0.31717 0.56745 0.34260 0.59163 0.35873 1.1 0.49883 0.38575 0.57524 0.44993 0.65637 0.51978 0.74229 0.59578 0.79807 0.64628 0.83324 0.67860 1.2 0.66166 0.67504 0.76489 0.79189 0.87594 0.92140 0.99580 1.0655 1.0752 1.1634 1.1260 1.2271 1.3 0.84674 1.1343 0.98493 1.3426 1.1382 1.5799 1.3104 1.8529 1.4292 2.0437 1.5075 2.1703 1.4 1.0670 1.8570 1.2586 2.2263 1.4818 2.6593 1.7467 3.1704 1.9376 3.5331 2.0665 3.7744 1.5 1.3514 2.9812 1.6280 3.6141 1.9610 4.3526 2.3598 5.1928 2.6408 5.7507 2.8241 6.0980 1.55 1.5270 3.7375 1.8561 4.5327 2.2478 5.4291 2.6986 6.3807 3.1822 7.2876 1.6 1.7241 4.6302 2.1035 5.5794 2.5374 6.5810 2.9994 7.5301 3.2785 8.0287 3.4389 8.2818 1.65 1.9349 5.6395 2.3500 6.6972 2.7926 7.7070 3.2165 8.5248 3.5668 9.0276 1.7 2.1441 6.7230 2.5689 7.8106 2.9823 8.7242 3.3341 9.3367 3.5045 9.5425 3.5889 9.6068 1.75 2.3332 7.8265 2.7388 8.8607 3.0963 9.6168 3.3701 10.037 3.5513 10.167 1.8 2.4872 8.9084 2.8521 9.8371 3.1472 10.443 3.3584 10.749 3.4512 10.832 3.4965 10.859 1.85 2.5999 9.9606 2.9165 10.784 3.1589 11.304 3.3313 11.606 3.4542 11.817 1.9 2.6753 11.015 2.9.186 11.784 3.1562 12.318 3.3136 12.738 3.3962 13.003 3.4444 13.183 1.95 2.7241 12.136 2.9668 12.939 3.1594 13.606 3.3231 14.284 3.4830 15.128 2.0 2.7594 13.406 2.9872 14.356 3.1840 15.299 3.3745 16.410 3.5017 17.270 3.5872 17.891 2.05 2.7938 14.922 3.0234 16.158 3.2433 17.553 3.4827 19.334 3.7777 21.790 2.1 2.8384 16.790 3.0867 18.483 3.3500 20.558 3.6642 23.322 3.9040 25.546 4.0742 27.151 2.15 2.9030 19.129 3.1877 21.490 3.5165 24.526 3.9315 28.607 4.4693 33.958 2.2 2.9960 22.070 3.3359 25.348 3.7510 29.624 4.2754 35.121 4.6499 38.949 4.8834 41.241 2.25 3.1250 25.746 3.5370 30.177 4.0455 35.778 4.6371 42.090 5.1699 47.081 2.3 3.2940 30.249 3.7852 35.922 4.3593 42.413 4.9128 48.055 5.1529 49.916 5.2368 50.181 2.35 3.5000 35.549 4.0544 42.186 4.6212 48.456 5.0250 51.868 5.1227 50.938 2.4 3.7273 41.395 4.2975 48.214 4.7683 52.923 4.9813 53.551 4.9693 51.967 4.9188 50.477 2.5 4.1223 52.611 4.5386 56.772 4.7137 56.846 4.6620 53.649 4.5551 50.775 4.4733 48.870 2.6 4.2736 60.249 4.4576 60.543 4.4453 57.728 4.3115 53.361 4.2010 50.466 4.1310 48.754 2.8 4.0837 69.125 4.0962 67.186 4.0780 65.482 4.1171 66.251 4.2214 69.419 4.3334 72.942 3.0 4.0732 90.929 4.3348 99.992 4.7320 115.28 4.9733 125.34 4.8277 120.45 4.6413 113.78 3.2 4.6996 149.37 4.8672 155.29 4.6106 142.17 4.1369 120.46 3.8151 106.35 3.6153 97.758 3.4 4.5617 173.90 4.2378 153.55 3.7896 127.99 3.3073 100.97 3.0471 85.853 2.9295 78.474 3.6 4.0134 170.72 3.6667 144.91 3.4395 127.56 3.6163 141.29 3.6583 152.46 3.4256 142.64 3.8 3.9050 199.25 4.0305 215.06 3.7904 206.09 3.0915 151.44 2.7514 123.10 2.5882 109.53 4.0 4.1885 290.97 3.6412 239.68 3.0438 182.26 2.4802 130.39 2.1253 97.911 1.9235 78.726 4.2 3.5754 279.25 2.9588 208.68 2.3349 136.04 2.0002 86.170 2.5506 133.16 4.4 2.9799 239.88 2.5395 169.85 2.7075 185.84 2.0937 125.80 1.7789 77.562 4.6 3.0884 286.24 2.7330 249.18 2.1567 154.28 2.0424 126.18 1.8758 103.44 4.8 2.8070 315.87 2.3152 218.50 1.9334 150.48 1.5371 82.730 2.0123 146.97 5.0 2.3677 280.53 1.8154 162.12 1.6497 106.77 2.0751 171.41 1.8539 138.28 5.2 1.9419 203.75 2.1580 218.91 1.7222 138.86 1.9616 184.21 2.6346 324.29 5.4 2.2210 298.14 1.7945 176.31 2.1228 239.93 2.1188 238.74 2.2176 288.93 5.6 1.9516 255.29 1.9299 235.00 1.7563 190.54 2.7738 503.19 2.5550 411.80 5.8 1.7446 234.73 1.6650 199.41 2.2189 348.99 2.3702 423.89 3.1203 722.67 6.0 1.8429 276.09 1.8634 282.08 2.3221 480.48 3.1456 806.24 2.7847 630.31 1 For definitions see, e.g., R. 0. Gumprecht and C. M. Particles (University of Michigan Press, Ann Arbor, Michigan, 2 E. J. Meehan and W. H. Beattie, J. Opt. Soc. Am. 49, 735 3 R. D. Murley, J. Phys. Chem. 64, 161 (1960). Sliepcevich, Tables of 1951), pp. x-xii. (1959). Light Scattering Functions for Spherical 260 VOLUME 51, NUMBER 3 MARCH, 1961
Transcript of Light Scattering Functions for Spherical Particles with m = 165 (005) 185
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA
Light Scattering Functions for Spherical Particles withm=1.65 (0.05) 1.85
E. J. MEEHAN AND Z Z. HUGUSSc/tool of Cheinistry, University of Minnesota, Minneapolis, Minnesota
(Received September 13, 1960)
Mie theory calculations are presented for scattering coefficient and forward scattering by sphericalparticles with in= 1.65 (0.05) 1.85 and a up to 6.0.
IN connection with certain light-scattering studies,Mie theory calculations were required for values
of the refractive index ratio in in the range 1.65-1.85.A few values of the scattering coefficient K and forwardscattering i(0) have been obtained previously byhand calculation for ,= 1.75 and 15 values of a up to3.6.2 The present calculations for in = 1.65 (0.05) 1.85 and48 values of ae up to 6.0 were carried out on a UnivacScientific (1103) computer. The computer programwas arranged to terminate when the absolute value ofthe largest of the four quantities R(An), I(An), R(Pn),and I(Pn) became smaller than 5X10-. Values of Kand i(0) were obtained to seven figures, and all the
values have been uniformly rounded to five figures inTable I. From the results it appears that the spacingof m(0.05) is close enough to permit reliable interpo-lation to intermediate m up to an a of about 3.0. Allthe hand-calculated values of K reported previouslyfor i= 1.75 have been confirmed, with the exception ofthat for a= 1.8, which was in error by -1.9%.
While these calculations were under way some valuesof K for in= 1.831 were published in graphical form. 3
It appeared of interest to extend these calculations,and accordingly some values of K and i(0) for m= 1.831are included in Table I.
TAnLE I. Values of K and i(0).
inI =1.65 . I =1.70 in =1.75 in =1.80 in =1.831 n =1.85a K i (O) K it (0) K i () K i (0) K it (0) K it (0)
0.5 0.023022 0.0024303 0.026072 0.0027585 0.029209 0.0030975 0.032415 0.0034460 0.034432 0.0036661 0.035677 0.00380240.6 0.048231 0.0077004 0.054811 0.0087778 0.061612 0.0098990 0.068602 0.011060 0.073017 0.011797 0.075749 0.0122550.7 0.089905 0.020672 0.10255 0.023675 0.11570 0.026825 0.12929 0.030111 0.13791 0.032213 0.14326 0.0335240.8 0.15312 0.049020 0.17530 0.056411 0.19848 0.064226 0.22258 0.072450 0.23795 0.077748 0.24751 0.0810690.9 0.24190 0.10533 0.27781 0.12177 0.31555 0.13931 0.35498 0.15792 0.38022 0.17001 0.39598 0.177631.0 0.35774 0.20859 0.41183 0.24220 0.46891 0.27837 0.52887 0.31717 0.56745 0.34260 0.59163 0.358731.1 0.49883 0.38575 0.57524 0.44993 0.65637 0.51978 0.74229 0.59578 0.79807 0.64628 0.83324 0.678601.2 0.66166 0.67504 0.76489 0.79189 0.87594 0.92140 0.99580 1.0655 1.0752 1.1634 1.1260 1.22711.3 0.84674 1.1343 0.98493 1.3426 1.1382 1.5799 1.3104 1.8529 1.4292 2.0437 1.5075 2.17031.4 1.0670 1.8570 1.2586 2.2263 1.4818 2.6593 1.7467 3.1704 1.9376 3.5331 2.0665 3.77441.5 1.3514 2.9812 1.6280 3.6141 1.9610 4.3526 2.3598 5.1928 2.6408 5.7507 2.8241 6.09801.55 1.5270 3.7375 1.8561 4.5327 2.2478 5.4291 2.6986 6.3807 3.1822 7.28761.6 1.7241 4.6302 2.1035 5.5794 2.5374 6.5810 2.9994 7.5301 3.2785 8.0287 3.4389 8.28181.65 1.9349 5.6395 2.3500 6.6972 2.7926 7.7070 3.2165 8.5248 3.5668 9.02761.7 2.1441 6.7230 2.5689 7.8106 2.9823 8.7242 3.3341 9.3367 3.5045 9.5425 3.5889 9.60681.75 2.3332 7.8265 2.7388 8.8607 3.0963 9.6168 3.3701 10.037 3.5513 10.1671.8 2.4872 8.9084 2.8521 9.8371 3.1472 10.443 3.3584 10.749 3.4512 10.832 3.4965 10.8591.85 2.5999 9.9606 2.9165 10.784 3.1589 11.304 3.3313 11.606 3.4542 11.8171.9 2.6753 11.015 2.9.186 11.784 3.1562 12.318 3.3136 12.738 3.3962 13.003 3.4444 13.1831.95 2.7241 12.136 2.9668 12.939 3.1594 13.606 3.3231 14.284 3.4830 15.1282.0 2.7594 13.406 2.9872 14.356 3.1840 15.299 3.3745 16.410 3.5017 17.270 3.5872 17.8912.05 2.7938 14.922 3.0234 16.158 3.2433 17.553 3.4827 19.334 3.7777 21.7902.1 2.8384 16.790 3.0867 18.483 3.3500 20.558 3.6642 23.322 3.9040 25.546 4.0742 27.1512.15 2.9030 19.129 3.1877 21.490 3.5165 24.526 3.9315 28.607 4.4693 33.9582.2 2.9960 22.070 3.3359 25.348 3.7510 29.624 4.2754 35.121 4.6499 38.949 4.8834 41.2412.25 3.1250 25.746 3.5370 30.177 4.0455 35.778 4.6371 42.090 5.1699 47.0812.3 3.2940 30.249 3.7852 35.922 4.3593 42.413 4.9128 48.055 5.1529 49.916 5.2368 50.1812.35 3.5000 35.549 4.0544 42.186 4.6212 48.456 5.0250 51.868 5.1227 50.9382.4 3.7273 41.395 4.2975 48.214 4.7683 52.923 4.9813 53.551 4.9693 51.967 4.9188 50.4772.5 4.1223 52.611 4.5386 56.772 4.7137 56.846 4.6620 53.649 4.5551 50.775 4.4733 48.8702.6 4.2736 60.249 4.4576 60.543 4.4453 57.728 4.3115 53.361 4.2010 50.466 4.1310 48.7542.8 4.0837 69.125 4.0962 67.186 4.0780 65.482 4.1171 66.251 4.2214 69.419 4.3334 72.9423.0 4.0732 90.929 4.3348 99.992 4.7320 115.28 4.9733 125.34 4.8277 120.45 4.6413 113.783.2 4.6996 149.37 4.8672 155.29 4.6106 142.17 4.1369 120.46 3.8151 106.35 3.6153 97.7583.4 4.5617 173.90 4.2378 153.55 3.7896 127.99 3.3073 100.97 3.0471 85.853 2.9295 78.4743.6 4.0134 170.72 3.6667 144.91 3.4395 127.56 3.6163 141.29 3.6583 152.46 3.4256 142.643.8 3.9050 199.25 4.0305 215.06 3.7904 206.09 3.0915 151.44 2.7514 123.10 2.5882 109.534.0 4.1885 290.97 3.6412 239.68 3.0438 182.26 2.4802 130.39 2.1253 97.911 1.9235 78.7264.2 3.5754 279.25 2.9588 208.68 2.3349 136.04 2.0002 86.170 2.5506 133.164.4 2.9799 239.88 2.5395 169.85 2.7075 185.84 2.0937 125.80 1.7789 77.5624.6 3.0884 286.24 2.7330 249.18 2.1567 154.28 2.0424 126.18 1.8758 103.444.8 2.8070 315.87 2.3152 218.50 1.9334 150.48 1.5371 82.730 2.0123 146.975.0 2.3677 280.53 1.8154 162.12 1.6497 106.77 2.0751 171.41 1.8539 138.285.2 1.9419 203.75 2.1580 218.91 1.7222 138.86 1.9616 184.21 2.6346 324.295.4 2.2210 298.14 1.7945 176.31 2.1228 239.93 2.1188 238.74 2.2176 288.935.6 1.9516 255.29 1.9299 235.00 1.7563 190.54 2.7738 503.19 2.5550 411.805.8 1.7446 234.73 1.6650 199.41 2.2189 348.99 2.3702 423.89 3.1203 722.676.0 1.8429 276.09 1.8634 282.08 2.3221 480.48 3.1456 806.24 2.7847 630.31
1 For definitions see, e.g., R. 0. Gumprecht and C. M.Particles (University of Michigan Press, Ann Arbor, Michigan,
2 E. J. Meehan and W. H. Beattie, J. Opt. Soc. Am. 49, 7353 R. D. Murley, J. Phys. Chem. 64, 161 (1960).
Sliepcevich, Tables of1951), pp. x-xii.(1959).
Light Scattering Functions for Spherical
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VOLUME 51, NUMBER 3 MARCH, 1961
