702:
36:
133:
669:
140:. Red crosses show measured values. Over the visible region (red shading), Cauchy's equation (blue line) agrees well with the measured refractive indices and the Sellmeier plot (green dashed line). It deviates in the ultraviolet and infrared regions.
497:
265:
360:
472:, the equation becomes inaccurate, and it cannot represent regions of anomalous dispersion. Despite this, its mathematical simplicity makes it useful in some applications.
460:
The theory of light-matter interaction on which Cauchy based this equation was later found to be incorrect. In particular, the equation is only valid for regions of normal
664:{\displaystyle n_{air}(\lambda ,T,v,p)\approx 1+{\frac {77.6\cdot 10^{-6}}{T}}\left(1+{\frac {7.52\cdot 10^{-3}}{\lambda ^{2}}}\right)\left(p+4810{\frac {v}{T}}\right)}
809:
290:
that can be determined for a material by fitting the equation to measured refractive indices at known wavelengths. The coefficients are usually quoted for λ as the
186:
479:
is a later development of Cauchy's work that handles anomalously dispersive regions, and more accurately models a material's refractive index across the
814:
701:
53:
119:
100:
72:
736:
20:
307:
799:
57:
79:
86:
46:
68:
24:
687:
153:
759:
169:
165:
461:
715:
476:
93:
491:
Cauchy's two-term equation for air, expanded by
Lorentz to account for humidity, is as follows:
291:
172:, who originally defined it in 1830 in his article "The refraction and reflection of light".
465:
157:
804:
260:{\displaystyle n(\lambda )=A+{\frac {B}{\lambda ^{2}}}+{\frac {C}{\lambda ^{4}}}+\cdots ,}
707:
793:
378:
480:
287:
132:
35:
697:
295:
161:
137:
760:"The Earth's atmosphere: seeing, background, absorption & scattering"
469:
739:. Bulletin de Ferussae, Volume XIV, p. 6-10 (1831) Original in French
376:
A table of coefficients for common optical materials is shown below:
145:
301:
Usually, it is sufficient to use a two-term form of the equation:
131:
29:
373:
are determined specifically for this form of the equation.
355:{\displaystyle n(\lambda )=A+{\frac {B}{\lambda ^{2}}},}
16:
Relationship between the refractive index and wavelength
500:
310:
189:
60:. Unsourced material may be challenged and removed.
663:
354:
259:
737:"Sur la réfraction et la réflexion de la lumière"
274:is the refractive index, λ is the wavelength,
180:The most general form of Cauchy's equation is
8:
168:material. It is named for the mathematician
646:
619:
605:
592:
566:
553:
505:
499:
341:
332:
309:
240:
231:
220:
211:
188:
120:Learn how and when to remove this message
727:
810:Electric and magnetic fields in matter
7:
786:, 4th ed., McGraw-Hill, Inc. (1981).
136:Refractive index vs. wavelength for
58:adding citations to reliable sources
682:is the temperature in kelvin, and
483:, visible, and infrared spectrum.
14:
678:is the air pressure in millibar,
700:
34:
45:needs additional citations for
815:Eponymous equations of physics
541:
517:
320:
314:
199:
193:
150:Cauchy's transmission equation
1:
782:F.A. Jenkins and H.E. White,
21:Cauchy's functional equation
487:Humidity dependence for air
833:
164:of light for a particular
18:
735:Cauchy, Augustin-Louis.
437:Barium flint glass BaF10
25:Cauchy momentum equation
19:Not to be confused with
688:vapor pressure of water
426:Barium crown glass BaK4
365:where the coefficients
784:Fundamentals of Optics
665:
448:Dense flint glass SF10
404:Borosilicate glass BK7
356:
261:
154:empirical relationship
141:
800:Augustin-Louis Cauchy
666:
357:
262:
170:Augustin-Louis Cauchy
135:
498:
308:
187:
54:improve this article
415:Hard crown glass K5
69:"Cauchy's equation"
716:Sellmeier equation
661:
477:Sellmeier equation
466:visible wavelength
352:
257:
142:
654:
625:
579:
458:
457:
347:
292:vacuum wavelength
246:
226:
130:
129:
122:
104:
822:
775:
774:
772:
770:
764:
755:
749:
748:
746:
744:
732:
710:
705:
704:
670:
668:
667:
662:
660:
656:
655:
647:
631:
627:
626:
624:
623:
614:
613:
612:
593:
580:
575:
574:
573:
554:
516:
515:
379:
361:
359:
358:
353:
348:
346:
345:
333:
266:
264:
263:
258:
247:
245:
244:
232:
227:
225:
224:
212:
158:refractive index
125:
118:
114:
111:
105:
103:
62:
38:
30:
832:
831:
825:
824:
823:
821:
820:
819:
790:
789:
779:
778:
768:
766:
762:
758:Trager, Scott.
757:
756:
752:
742:
740:
734:
733:
729:
724:
706:
699:
696:
636:
632:
615:
601:
594:
585:
581:
562:
555:
501:
496:
495:
489:
468:region. In the
337:
306:
305:
236:
216:
185:
184:
178:
126:
115:
109:
106:
63:
61:
51:
39:
28:
17:
12:
11:
5:
830:
829:
826:
818:
817:
812:
807:
802:
792:
791:
788:
787:
777:
776:
750:
726:
725:
723:
720:
719:
718:
712:
711:
708:Physics portal
695:
692:
672:
671:
659:
653:
650:
645:
642:
639:
635:
630:
622:
618:
611:
608:
604:
600:
597:
591:
588:
584:
578:
572:
569:
565:
561:
558:
552:
549:
546:
543:
540:
537:
534:
531:
528:
525:
522:
519:
514:
511:
508:
504:
488:
485:
456:
455:
452:
449:
445:
444:
441:
438:
434:
433:
430:
427:
423:
422:
419:
416:
412:
411:
408:
405:
401:
400:
397:
394:
390:
389:
386:
383:
363:
362:
351:
344:
340:
336:
331:
328:
325:
322:
319:
316:
313:
268:
267:
256:
253:
250:
243:
239:
235:
230:
223:
219:
215:
210:
207:
204:
201:
198:
195:
192:
177:
174:
128:
127:
42:
40:
33:
15:
13:
10:
9:
6:
4:
3:
2:
828:
827:
816:
813:
811:
808:
806:
803:
801:
798:
797:
795:
785:
781:
780:
765:. S.C. Trager
761:
754:
751:
738:
731:
728:
721:
717:
714:
713:
709:
703:
698:
693:
691:
690:in millibar.
689:
685:
681:
677:
657:
651:
648:
643:
640:
637:
633:
628:
620:
616:
609:
606:
602:
598:
595:
589:
586:
582:
576:
570:
567:
563:
559:
556:
550:
547:
544:
538:
535:
532:
529:
526:
523:
520:
512:
509:
506:
502:
494:
493:
492:
486:
484:
482:
478:
473:
471:
467:
463:
453:
450:
447:
446:
442:
439:
436:
435:
431:
428:
425:
424:
420:
417:
414:
413:
409:
406:
403:
402:
398:
395:
392:
391:
387:
384:
381:
380:
377:
374:
372:
368:
349:
342:
338:
334:
329:
326:
323:
317:
311:
304:
303:
302:
299:
297:
293:
289:
286:, etc., are
285:
281:
277:
273:
254:
251:
248:
241:
237:
233:
228:
221:
217:
213:
208:
205:
202:
196:
190:
183:
182:
181:
175:
173:
171:
167:
163:
159:
155:
151:
147:
139:
134:
124:
121:
113:
110:November 2022
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
26:
22:
783:
767:. Retrieved
753:
741:. Retrieved
730:
683:
679:
675:
673:
490:
474:
459:
393:Fused silica
375:
370:
366:
364:
300:
288:coefficients
283:
279:
275:
271:
269:
179:
176:The equation
156:between the
149:
143:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
481:ultraviolet
296:micrometres
166:transparent
794:Categories
722:References
462:dispersion
162:wavelength
80:newspapers
617:λ
607:−
599:⋅
568:−
560:⋅
545:≈
521:λ
339:λ
318:λ
252:⋯
238:λ
218:λ
197:λ
138:BK7 glass
743:28 April
694:See also
470:infrared
454:0.01342
443:0.00743
432:0.00531
421:0.00459
410:0.00420
399:0.00354
382:Material
686:is the
464:in the
388:B (μm)
94:scholar
805:Optics
769:31 May
674:where
451:1.7280
440:1.6700
429:1.5690
418:1.5220
407:1.5046
396:1.4580
270:where
152:is an
146:optics
96:
89:
82:
75:
67:
763:(PDF)
101:JSTOR
87:books
771:2022
745:2024
644:4810
596:7.52
557:77.6
475:The
369:and
160:and
73:news
294:in
144:In
56:by
23:or
796::
603:10
564:10
298:.
282:,
278:,
148:,
773:.
747:.
684:v
680:T
676:p
658:)
652:T
649:v
641:+
638:p
634:(
629:)
621:2
610:3
590:+
587:1
583:(
577:T
571:6
551:+
548:1
542:)
539:p
536:,
533:v
530:,
527:T
524:,
518:(
513:r
510:i
507:a
503:n
385:A
371:B
367:A
350:,
343:2
335:B
330:+
327:A
324:=
321:)
315:(
312:n
284:C
280:B
276:A
272:n
255:,
249:+
242:4
234:C
229:+
222:2
214:B
209:+
206:A
203:=
200:)
194:(
191:n
123:)
117:(
112:)
108:(
98:·
91:·
84:·
77:·
50:.
27:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
