Table I
Coefficients for Standard System I′ [λ1 = 0.644 (C′); λ2 = 0.480 (F′)] and for λm = 0.546 (e) and 0.587 (d), Respectively
λ(nm) | 1 − Dx | Bx | 1 −
|
| 1 −
|
|
---|
334.1 | 0.980397 | 4.67875 | 0.979881 | 4.22862 | 0.979994 | 4.45369 |
365.0(i) | 0.990545 | 3.25251 | 0.990023 | 2.79779 | 0.990138 | 3.02512 |
377.6(T1) | 0.992955 | 2.83855 | 0.992432 | 2.38272 | 0.992547 | 2.61062 |
390.0 | 0.994772 | 2.49094 | 0.994248 | 2.03427 | 0.994363 | 2.26258 |
404.6(h) | 0.996387 | 2.14322 | 0.995862 | 1.68581 | 0.995978 | 1.91450 |
435.8(g) | 0.998565 | 1.56702 | 0.998039 | 1.10861 | 0.998155 | 1.33779 |
| | | | |
480.0(F′) | 1. — | 1. — | 0.999473 | 0.54093 | 0.999589 | 0.77044 |
|
| | | | |
486.1(F) | 1.000108 | 0.93717 | 0.999581 | 0.47805 | 0.999697 | 0.70759 |
| | |
| | |
546.0(e) | 1.000527 | 0.45931 | 1. — | 0. — | 1.000116 | 0.22963 |
| | |
|
587.6(d) | 1.000411 | 0.22965 | 0.999884 | −0.22961 | 1. — | 0. — |
|
| | |
|
643.8(c) | 1. — | 0. — | 0.999473 | −0.45907 | 0.999589 | −0.22956 |
|
| | | | |
656.3(C) | 0.999884 | −0.04132 | 0.999357 | −0.50033 | 0.999473 | −0.27085 |
706.5(r) | 0.999356 | −0.18247 | 0.998830 | −0.64124 | 0.998945 | −0.41188 |
768.2A | 0.998613 | −0.31246 | 0.998087 | −0.77089 | 0.998203 | −0.54170 |
852.1(s) | 0.997494 | −0.43744 | 0.996960 | −0.89536 | 0.997084 | −0.66642 |
1,014.0(t) | 0.995066 | −0.57774 | 0.994542 | −1.03566 | 0.994657 | −0.80616 |
400 | 0.995926 | 2.24729 | 0.995401 | 1.7901 | 0.995516 | 2.01868 |
410 | 0.996864 | 2.03032 | 0.996340 | 1.57269 | 0.996454 | 1.80148 |
420 | 0.997630 | 1.83601 | 0.997105 | 1.37803 | 0.997220 | 1.60700 |
430 | 0.998255 | 1.66114 | 0.997730 | 1.20287 | 0.997844 | 1.43199 |
440 | 0.998765 | 1.50307 | 0.998239 | 1.04456 | 0.998354 | 1.27380 |
450 | 0.999179 | 1.35959 | 0.998654 | 0.90090 | 0.998769 | 1.13023 |
460 | 0.999515 | 1.22890 | 0.998989 | 0.77005 | 0.999104 | 0.99946 |
470 | 0.999785 | 1.10944 | 0.999259 | 0.65046 | 0.999374 | 0.87993 |
480 | 1. — | 0.99991 | 0.999474 | 0.54084 | 0.999589 | 0.77035 |
490 | 1.000168 | 0.89920 | 0.999642 | 0.44005 | 0.999757 | 0.66960 |
500 | 1.000297 | 0.80635 | 0.999771 | 0.34714 | 0.999886 | 0.57673 |
510 | 1.000393 | 0.72054 | 0.999866 | 0.36129 | 0.999981 | 0.49090 |
520 | 1.000460 | 0.64106 | 0.999933 | 0.18178 | 1.000048 | 0.41141 |
530 | 1.000502 | 0.56729 | 0.999975 | 0.10799 | 1.000090 | 0.33762 |
540 | 1.000523 | 0.49867 | 0.999996 | 0.03936 | 1.000111 | 0.26900 |
550 | 1.000526 | 0.43473 | 0.999999 | −0.02458 | 1.000114 | 0.20506 |
560 | 1.000513 | 0.37504 | 0.999986 | −0.08426 | 1.000101 | 0.14537 |
570 | 1.000486 | 0.31924 | 0.999960 | −0.14005 | 1.000075 | 0.08958 |
580 | 1.000448 | 0.26699 | 0.999921 | −0.19229 | 1.000036 | 0.03733 |
590 | 1.000399 | 0.21799 | 0.999872 | −0.24127 | 0.999987 | −0.01166 |
600 | 1.000340 | 0.17197 | 0.999814 | −0.28725 | 0.999929 | −0.05766 |
610 | 1.000274 | 0.12871 | 0.999747 | −0.33049 | 0.999862 | −0.10091 |
620 | 1.000200 | 0.08798 | 0.999674 | −0.37118 | 0.999789 | −0.14162 |
630 | 1.000120 | 0.04960 | 0.999594 | −0.40953 | 0.999709 | −0.17998 |
640 | 1.000034 | 0.01339 | 0.999508 | −0.44570 | 0.999623 | −0.21617 |
650 | 0.999944 | −0.02081 | 0.999417 | −0.47985 | 0.999533 | −0.25035 |
675 | 0.999697 | −0.09842 | 0.999170 | −0.55735 | 0.999286 | −0.31991 |
700 | 0.999429 | −0.16621 | 0.998903 | −0.62502 | 0.999018 | −0.39563 |
750 | 0.998841 | −0.27815 | 0.998315 | −0.73669 | 0.998431 | −0.50744 |
800 | 0.998202 | −0.36567 | 0.997676 | −0.82391 | 0.997792 | −0.59481 |
900 | 0.996810 | −0.48998 | 0.996285 | −0.94758 | 0.996400 | −0.71880 |
1000 | 0.995289 | −0.56924 | 0.994765 | −1.02615 | 0.994880 | −0.79771 |
Table II
Glass Type SF 58
λ (nm) | I | II | III | IV | V | Refractive Index Difference × 106 |
---|
II-I | III-I | IV-I | V-I |
---|
405 | 1.999230 | 231 | 231 | 054 | 8587 | 1 | 1 | −(176) | −(643) |
|
| | |
| | | |
| |
436 | 1.974855 | 860 | 860 | 855 | 735 | 5 | 5 | 0 | −(120) |
|
| | |
| | | |
| |
440 | 1.972153 | — | 156 | 157 | 063 | — | 2 | 3 | −(91) |
| | | | |
| | | |
|
460 | 1.960551 | — | 552 | 560 | 550 | — | 1 | +8 | 2 |
| | |
|
| | |
|
|
480 | 1.950835 | 836 | 836 | 835 | 863 | 1 | 1 | 0 | 28 |
| | |
| | | |
|
500 | 1.942579 | — | 580 | 575 | 606 | | 1 | −4 | 27 |
520 | 1.935494 | — | 495 | 489 | 510 | | 1 | −5 | 16 |
|
546 | 1.927647 | 647 | 647 | 647 | 647 | 0 | 0 | 0 | 0 |
|
560 | 1.923984 | — | 984 | 986 | 977 | — | 0 | +2 | −7 |
588 | 1.917612 | 613 | 613 | 622 | 603 | 1 | 1 | +10 | −9 |
600 | 1.915064 | — | 065 | 075 | 058 | — | 1 | +11 | −6 |
620 | 1.911328 | — | 328 | 337 | 333 | — | 0 | +9 | +5 |
| | |
| | | |
| |
644 | 1.907374 | 375 | 375 | 374 | 402 | 1 | 1 | 0 | +28 |
| | |
| | | |
|
656 | 1.905501 | 503 | 503 | 492 | 544 | 2 | 2 | −9 | +(43) |
707 | 1.898997 | 999 | 999 | 919 | 9125 | 2 | 2 | −(78) | (128) |
852 | 1.886475 | 480 | 482 | — | 7043 | 5 | 7 | — | (568) |
1014 | 1.878311 | 320 | 319 | — | 9641 | 9 | 8 | — | (1330) |
Comparison of experimental
nx values and those calculated by different formulas for some glasses of different types as to the behavior of the 5 curve (see
Figs. 3–
5).
The columns have the following meaning: 1, wavelength (nm); I, values derived from the probable smoothed
δ curve; II, values of the catalogs or direct measurements taken in the test laboratory of JENAer GLASWERK; III, values calculated by the six-constant- dispersion formula from the catalog 3050; IV, values calculated according to
Eq. (7), i.e., corresponding to a
δx curve linear with the wavelength and drawn through the curve points for
g and
e; V, values calculated according to
Eq. (8), i.e., corresponding to a single
δz0 constant, the latter being the value for 500 nm of the
δ curve.
I-II, etc. signify the difference of the respective columns and the probable values given in I.
In
table III cols. II and III are missing, because the composition of the investigated melt was somewhat different compared with the normal glass type.
From col. II only the last three figures are given.
Table III
SF 3 (Deviating Melt)
λ (nm) | I | IV | V | IV-I | V-I |
---|
365 | 1.814548 | 319 | 041 | −(229) | −(507) |
400 | 1.790944 | 905 | 818 | −(39) | −(126) |
405 | 1.788447 | 413 | 341 | −(34) | −(106) |
| |
| |
436 | 1.774455 | 455 | 434 | 0 | −21 |
| |
| |
440 | 1.772879 | 880 | 862 | 1 | −17 |
| | |
| |
|
460 | 1.766051 | 054 | 050 | 3 | −1 |
|
|
|
|
480 | 1.760265 | 265 | 269 | 0 | 4 |
| |
|
500 | 1.755299 | 298 | 303 | −1 | 4 |
520 | 1.751001 | 001 | 004 | 0 | 3 |
|
546 | 1.746202 | 202 | 202 | 0 | 0 |
|
560 | 1.743946 | 947 | 946 | +1 | 0 |
588 | 1.740002 | 003 | 001 | +1 | −1 |
600 | 1.738416 | 418 | 415 | +2 | −1 |
620 | 1.736082 | 083 | 082 | +1 | 0 |
| |
| |
644 | 1.733599 | 599 | 603 | 0 | 4 |
| |
|
656 | 1.732418 | 417 | 424 | −1 | 6 |
707 | 1.728291 | 277 | 309 | −14 | 18 |
852 | 1.720186 | 074 | 270 | −(112) | (84) |
1014 | 1.714702 | — | 913 | — | (211) |
Table IV
Glass Type F 11
λ (nm) | I | II | III | IV | V | II-I | III-I | IV-I | V-I |
---|
365 | 1.669079 | 080 | 076 | | 8254 | 1 | −3 | | −(825) |
400 | 1.653949 | — | 953 | | 746 | | 4 | | −(203) |
405 | 1.652359 | 357 | 357 | | 184 | −2 | −2 | | −(175) |
| | |
| | | |
| |
436 | 1.643381 | 376 | 376 | 381 | 346 | −5 | −4 | 0 | −(35) |
| | |
| | | |
| |
440 | 1.642366 | — | 362 | 369 | 340 | | −4 | 3 | −26 |
| | | | |
| | | |
|
460 | 1.637967 | — | 965 | 970 | 967 | | −2 | 3 | 0 |
| | |
|
| | |
|
|
480 | 1.634226 | 225 | 225 | 226 | 233 | −1 | −1 | 0 | +7 |
| | |
| | | |
|
|
500 | 1.631001 | — | 002 | 001 | 009 | | 1 | 0 | +8 |
520 | 1.628199 | — | 200 | 198 | 204 | | 1 | −1 | +5 |
|
546 | 1.625055 | 055 | 055 | 055 | 055 | 0 | 0 | 0 | 0 |
|
560 | 1.623570 | — | 571 | 571 | 569 | | 1 | +1 | −1 |
588 | 1.620962 | 962 | 962 | 964 | 959 | 0 | 0 | +2 | −3 |
600 | 1.619908 | — | 908 | 911 | 906 | | 0 | +3 | −2 |
620 | 1.618350 | — | 350 | 351 | 352 | | 0 | +1 | +2 |
| | |
| | | |
| |
644 | 1.616685 | 684 | 684 | 685 | 692 | −1 | −1 | 0 | +7 |
| | |
| | | |
|
|
656 | 1.615888 | 888 | 888 | 888 | 900 | 0 | 0 | 0 | +12 |
707 | 1.613080 | 080 | 080 | | 118 | 0 | 0 | | +38 |
852 | 1.607391 | 390 | 394 | | 564 | −1 | 3 | | (173) |
1014 | 1.603286 | 280 | 279 | | 693 | −6 | −7 | | (413) |
Table V
Glass Type BaSF 13.
λ (nm) | I | II | III | IV | V | II-I | III-I | IV-I | V-I |
---|
365 | 1.746689 | 690 | 689 | 499 | 409 | 1 | 0 | −(190) | − (280) |
405 | 1.730037 | 043 | 043 | 016 | 9986 | 6 | 6 | −21 | −(51) |
| | |
| | | |
| |
436 | 1.720896 | 896 | 896 | 896 | 887 | 0 | 0 | 0 | −9 |
| | |
| | | |
| |
440 | 1.719857 | | 855 | 856 | 849 | | −2 | −1 | −8 |
| | | | |
| | | |
|
460 | 1.715327 | | 326 | 327 | 326 | | −1 | 0 | −1 |
| | |
|
| | |
|
|
480 | 1.711454 | 454 | 454 | 455 | 455 | 0 | 0 | 1 | +1 |
| | |
| | | |
|
|
500 | 1.708103 | | 104 | 103 | 104 | | 1 | 0 | +1 |
520 | 1.705183 | | 183 | 183 | 184 | | 0 | 0 | +1 |
|
546 | 1.701897 | 897 | 897 | 897 | 897 | 0 | 0 | 0 | 0 |
|
560 | 1.700343 | | 343 | 343 | 343 | | 0 | 0 | 0 |
588 | 1.697610 | 610 | 610 | 611 | 610 | 0 | 0 | 1 | 0 |
600 | 1.696505 | | 505 | 506 | 505 | | 0 | 1 | 0 |
620 | 1.694871 | | 872 | 872 | 871 | | 1 | 1 | 0 |
| | |
| | | |
| |
644 | 1.693124 | 124 | 124 | 124 | 125 | 0 | 0 | 0 | +1 |
| | |
| | | |
|
|
656 | 1.692289 | 289 | 289 | 288 | 290 | 0 | 0 | −1 | +1 |
707 | 1.689346 | 347 | 347 | 338 | 349 | 1 | 1 | −8 | +3 |
852 | 1.683419 | 420 | 420 | 362 | 428 | 1 | 1 | −(57) | +9 |
1014 | 1.679201 | 201 | 204 | — | 229 | 0 | 3 | — | +28 |
Table VI
Glass Type LF 5
λ (nm) | I | II | III | IV | V | II-I | III-I | IV-I | V-I |
---|
365 | 1.619239 | 238 | 238 | 234 | 258 | −1 | −1 | −5 | +19 |
400 | 1.607899 | — | 900 | 899 | 906 | | 1 | 0 | +7 |
405 | 1.606666 | 669 | 670 | 666 | 672 | +3 | 4 | 0 | +6 |
| | |
| | | |
| |
436 | 1.599638 | 638 | 638 | 638 | 640 | 0 | 0 | 0 | +2 |
| | |
| | | |
| |
440 | 1.598834 | — | 833 | 833 | 835 | | −1 | −1 | +1 |
| | | | |
| | | |
|
460 | 1.595320 | — | 320 | 320 | 320 | | 0 | 0 | 0 |
| | |
|
| | |
|
|
480 | 1.592304 | 304 | 304 | 304 | 304 | 0 | 0 | 0 | 0 |
| | |
| | | |
|
|
500 | 1.589686 | — | 686 | 686 | 686 | | 0 | 0 | 0 |
520 | 1.587399 | — | 398 | 399 | 398 | | −1 | 0 | −1 |
|
546 | 1.584818 | 818 | 818 | 818 | 818 | 0 | 0 | 0 | 0 |
|
560 | 1.583595 | — | 595 | 595 | 595 | | 0 | 0 | 0 |
588 | 1.581440 | 440 | 440 | 440 | 440 | 0 | 0 | 0 | 0 |
600 | 1.580567 | — | 567 | 567 | 568 | | 0 | 0 | +1 |
620 | 1.579275 | — | 275 | 275 | 275 | | 0 | 0 | 0 |
| | |
| | | |
| |
644 | 1.577891 | 891 | 891 | 891 | 891 | 0 | 0 | 0 | 0 |
| | |
| | | |
|
|
656 | 1.577228 | 229 | 228 | . 228 | 228 | +1 | 0 | 0 | 0 |
707 | 1.574888 | 890 | 888 | 888 | 885 | +2 | 0 | 0 | −3 |
852 | 1.570139 | 140 | 139 | 143 | 125 | +1 | 0 | 4 | −14 |
1014 | 1.566722 | 725 | 725 | — | 688 | +3 | 3 | — | −(34) |
Table VII
Glass Type BK 7
λ (nm) | I | II | III | IV | V | II-I | III-I | IV-I | V-I |
---|
365 | 1.536263 | 260 | 263 | 246 | 150 | −3 | 0 | −17 | −(113) |
400 | 1.530848 | — | 848 | 845 | 814 | | 0 | −3 | −(34) |
405 | 1.530239 | 240 | 240 | 237 | 212 | 1 | 1 | −2 | −27 |
| | |
| | | |
| |
436 | 1.526684 | 686 | 686 | 684 | 679 | 2 | 2 | 0 | −5 |
| | |
| | | |
| |
440 | 1.526269 | — | 270 | 269 | 265 | | 1 | 0 | −4 |
| | | | |
| | | |
|
460 | 1.524433 | — | 435 | 433 | 434 | | 2 | 0 | +1 |
| | |
|
| | |
|
|
480 | 1.522829 | 830 | 829 | 829 | 831 | 1 | 0 | 0 | +2 |
| | |
| | | |
|
|
500 | 1.521414 | — | 415 | 414 | 416 | | 1 | 0 | +2 |
520 | 1.520160 | — | 160 | 160 | 161 | | 0 | 0 | +1 |
|
546 | 1.518722 | 722 | 722 | 722 | 722 | 0 | 0 | 0 | 0 |
|
560 | 1.518032 | — | 032 | 032 | 031 | | 0 | 0 | −1 |
588 | 1.516800 | 800 | 800 | 800 | 799 | 0 | 0 | 0 | −1 |
600 | 1.516294 | — | 295 | 295 | 294 | | 1 | 1 | 0 |
620 | 1.515539 | — | 540 | 539 | 539 | | 1 | 0 | 0 |
| | |
| | | |
| |
644 | 1.514719 | 720 | 720 | 719 | 721 | 1 | 1 | 0 | +2 |
| | |
| | | |
|
|
656 | 1.514322 | 323 | 323 | 322 | 325 | 1 | 1 | 0 | +3 |
707 | 1.512893 | 894 | 894 | 892 | 904 | 1 | 1 | −1 | +11 |
852 | 1.509804 | 810 | 807 | 790 | 862 | 6 | 3 | −14 | +(58) |
1014 | 1.507311 | 310 | 313 | — | 453 | −1 | 2 | — | +(142) |
Table VIII
Glass Type LGSK 2
λ (nm) | I | II | A (500) | B (436) | II-I | A-I | B-I |
---|
365 | 1.613311 | 310 | 618 | 478 | −1 | (307) | (617) |
400 | 1.606385 | — | 474 | 410 | — | (89) | 25 |
405 | 1.605612 | 610 | 685 | 627 | −2 | (73) | 15 |
436 | 1.601117 | 110 | 132 | 104 | −7 | 15 | −13 |
440 | 1.600593 | — | 605 | 581 | — | 12 | −12 |
| | | | | |
| |
460 | 1.598294 | — | 293 | 279 | — | −1 | −15 |
| | | | |
| |
480 | 1.596296 | 300 | 292 | 284 | +4 | −4 | −12 |
| | | | |
|
|
500 | 1.594546 | — | 541 | 538 | — | −5 | −8 |
520 | 1.593004 | — | 000 | 000 | — | −4 | −4 |
|
546 | 1.591250 | 250 | 250 | 250 | 0 | 0 | 0 |
|
560 | 1.590415 | — | 416 | 415 | — | +1 | 0 |
588 | 1.588934 | 940 | 936 | 935 | +6 | +2 | 1 |
600 | 1.588333 | — | 334 | 332 | — | +1 | −1 |
620 | 1.587439 | — | 439 | 434 | — | 0 | −5 |
| | | | | | |
644 | 1.586478 | 480 | 474 | 466 | +2 | −4 | −12 |
| | | | |
|
|
656 | 1.586017 | 020 | 009 | 997 | +3 | −8 | −20 |
707 | 1.584383 | 380 | 356 | 340 | −3 | −27 | −(43) |
852 | 1.581045 | 050 | 0910 | 867 | +5 | −(135) | −(178) |
1014 | 1.578635 | 640 | 302 | 226 | +5 | −(333) | −(409) |
Comparison of the
nx values calculated by two different three-constant formulas according to
Eq. (8), column A using the number 100
δx0 = 8.0, corresponding to λ
0 = 500 nm, and B using 100
δx0 = 6.6, corresponding to λ
0 = 436 nm, respectively. Columns I and II, respectively, are the probable and the experimental values. It can be seen that in the important wavelength range between 440 nm and 707 nm the values of cols. A-I should be preferred to those of col. B-I.
Table IX
SSK N 5(Deviating Melt)
λnm | I | IV | V | IV-I | V-I |
---|
a 365 | 1.691364 | 376 | 465 | 13 | 101 |
b | | | 464 | | (100) |
a 400 | 1.681838 | 839 | 868 | 1 | (30) |
b | | | 867 | | (29) |
a 405 | 1.680785 | 786 | 810 | 1 | 25 |
b | | | 809 | | 24 |
a 436 | 1.674706 | 706 | 712 | 0 | 6 |
b | | 5 | 711 | −1 | 5 |
a 440 | 1.674003 | 003 | 008 | 0 | 5 |
b | | 2 | 007 | −1 | 4 |
a 460 | 1.670916 | 916 | 917 | 0 | 1 |
b | | | 916 | | 0 |
|
a 480 | 1.668244 | 244 | 243 | 0 | −1 |
b | | | 243 | | |
|
a 500 | 1.665908 | 908 | 907 | 0 | −1 |
b | | | 906 | | −2 |
a 520 | 1.663853 | 853 | 853 | 0 | 0 |
b | = 4 | | 852 | −1 | 2 |
a 546 | 1.661519 | 520 | 520 | 1 | 1 |
b | −20 | | 520 | 0 | 0 |
a 560 | 1.660408 | 408 | 409 | 0 | 1 |
b | = 9 | | 409 | −1 | 0 |
a 588 | 1.658440 | 440 | 441 | 0 | 1 |
b | | | 440 | | 0 |
a 600 | 1.657639 | 639 | 640 | 0 | 1 |
b | | | 639 | | 0 |
a 620 | 1.656449 | 449 | 450 | 0 | 1 |
b | | | 449 | | 0 |
|
644 | 1.655168 | 168 | 167 | 0 | −1 |
|
a 656 | 1.654553 | 553 | 551 | 0 | −2 |
b | | 2 | 550 | −1 | −3 |
a 707 | 1.652366 | 366 | 357 | 0 | −9 |
b | | | 356 | | −10 |
a 852 | 1.647846 | 853 | 796 | 7 | −(50) |
b | | 2 | 785 | 6 | −(49) |
a 1014 | 1.644486 | — | 361 | | −(125) |
b | | | 360 | | −(126) |
Comparison of the values of
nx calculated by means of the four-constant formula
Eq. (7) (col. IV) and the three-constant formula
Eq. (8) (col. V) using
δx0 = −0.40 and of the probable values given in I. The lines a and b, respectively, are calculated from
nm =
nd and
nm =
ne, respectively. It can be seen that the difference between a and b never exceeds the error 1 × 10
−6 caused by rounding. From 436 nm to 707 nm both formulas give excellent results.