Der Regenbogen in Wissenschaft und Kunst

S. Rösch

doi:10.1364/AO.7.000233

Applied Optics
Vol. 7,
Issue 2,
pp. 233-239
(1968)
•https://doi.org/10.1364/AO.7.000233

Der Regenbogen in Wissenschaft und Kunst

S. Rösch

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S. Rösch, "Der Regenbogen in Wissenschaft und Kunst," Appl. Opt. 7, 233-239 (1968)

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Abstract

New ideas and calculations about angles are presented, particularly about the degree of polarization of the first twenty rainbows, and it is proved why never more than two rainbows can be seen in the sky. The general sky brightness of the rainbow neighborhood is calculated with the Fresnel reflection formulas. It is shown that for certain refraction indices the first one or each of the higher rainbows can be polarized completely and that with a rising n there is an upper limit of existence for each one of them. This is clearly shown by diagrams. The standard of the exact color finding on rainbows is described with special emphasis on the fact that the loss of saturation, due to light reflected by waterdrops, must be considered. Some special features of rainbows mentioned in literature are pointed out and the importance of this phenomenon in constructive art, folklore, and religion is discussed.

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k	∊(k)	∊′(k)	D	τ_s(k)	τ_p(k)	I(k)	I_s(k)	I_p(k)
1	59° 21.1′	40° 09.6′	138° 03.8′	0.88890	0.99572	0.04601	0.08778	0.00425
2	71° 48.6′	45° 24.7′	231° 09.0′	0.75001	0.93480	0.01943	0.03516	0.00371
3	76° 49.3′	46° 52.6′	318° 38.2′	0.63989	0.85233	0.01073	0.01912	0.00234
4	79° 37.0′	47° 30.4′	U^a + 44° 10.0′	0.55557	0.77736	0.00680	0.01204	0.00157
5	81° 25.0′	47° 50.2′	U + 128° 47.6′	0.48982	0.70572	0.00469	0.00829	0.00110
6	82° 40.7′	48° 01.9′	U + 212° 54.8′	0.43751	0.64608	0.00344	0.00606	0.00082
7	83° 36.8′	48° 09.4′	U + 296° 43.2′	0.39504	0.59541	0.00263	0.00463	0.00063
8	84° 20.1′	48° 14.6′	2U + 20° 17.4′	0.35999	0.55131	0.00207	0.00365	0.00050
9	84° 54.6′	48° 18.2′	2U + 103° 45.2′	0.33209	0.51294	0.00169	0.00298	0.00041
10	85° 22.6′	48° 20.8′	2U + 187° 07.6′	0.30555	0.47945	0.00139	0.00244	0.00034
11	85° 45.9′	48° 22.8′	2U + 270° 24.6′	0.28372	0.44993	0.00117	0.00205	0.00028
12	86° 05.6′	48° 24.4′	2U + 353° 36.8′	0.26535	0.42371	0.00099	0.00174	0.00024
13	86° 22.5′	48° 25.7′	3U + 76° 45.4′	0.24888	0.40021	0.00085	0.00150	0.00021
14	86° 37.1′	48° 26.7′	3U + 159° 53.2′	0.23434	0.37922	0.00074	0.00131	0.00018
15	86° 49.8′	48° 27.5′	3U + 242° 59.6′	0.22150	0.36034	0.00065	0.00114	0.00016
16	87° 01.1′	48° 28.2′	3U + 326° 03.4′	0.20983	0.34304	0.00058	0.00102	0.00014
17	87° 11.1′	48° 28.8′	4U + 49° 05.4′	0.19939	0.32743	0.00052	0.00091	0.00013
18	87° 19.9′	48° 29.3′	4U + 132° 06.4′	0.09008	0.31334	0.00046	0.00081	0.00011
19	87° 28.0′	48° 29.7′	4U + 215° 08.0′	0.18138	0.30009	0.00042	0.00073	0.00010
20	87° 35.3′	48° 30.0′	4U + 298° 10.6′	0.17352	0.28800	0.00038	0.00067	0.00009

k	∊(ä)	ρ(ä)	ρ_s(ä)	ρ_p(ä)	I(k): ρ(ä)	I_s(k): ρ_s(ä)	I_p(k): p_p(ä)
1	20° 58.1′	0.02071	0.02507	0.01634	2.223	3.500	0.260
2	25° 34.5′	0.02100	0.02769	0.01433	0.926	1.270	0.260
3	69° 19.1′	0.12633	0.21003	0.04263	0.085	0.091	0.055
4	67° 55.0′	0.11141	0.19098	0.03184	0.061	0.063	0.049
5	25° 36.2′	0.02100	0.02772	0.01429	0.224	0.299	0.077
6	16° 27.4′	0.02057	0.02320	0.01794	0.167	0.261	0.046
7	58° 21.6′	0.05356	0.10485	0.00227	0.049	0.044	0.277
8	78° 51.3′	0.31038	0.41944	0.20132	0.0066	0.0087	0.0025
9	38° 07.4′	0.02446	0.04040	0.00853	0.069	0.074	0.048
10	03° 33.8′	0.02039	0.02053	0.02025	0.068	0.118	0.017
11	45° 12.3′	0.02820	0.05369	0.00272	0.041	0.038	0.104
12	86° 48.4′	0.70733	0.77709	0.63757	0.0014	0.0024	0.0004
13	51° 37.3′	0.03643	0.07273	0.00014	0.023	0.021	1.530
14	10° 03.4′	0.02049	0.02145	0.01953	0.036	0.061	0.0093
15	31° 29.8′	0.02181	0.03246	0.01116	0.030	0.035	0.014
16	72° 59.7′	0.17016	0.26697	0.07336	0.0034	0.0038	0.0019
17	65° 27.3′	0.09064	0.16224	0.01904	0.0057	0.0056	0.0066
18	23° 56.8′	0.02088	0.02668	0.01507	0.022	0.030	0.0076
19	17° 34.0′	0.02058	0.02359	0.01757	0.020	0.031	0.0058
20	59° 05.3′	0.05623	0.10938	0.00307	0.0067	0.0061	0.030

k	∊(k)	∊′(k)	D	τ_s(k)	τ_p(k)	I(k)	I_s(k)	I_p(k)
1	59° 21.1′	40° 09.6′	138° 03.8′	0.88890	0.99572	0.04601	0.08778	0.00425
2	71° 48.6′	45° 24.7′	231° 09.0′	0.75001	0.93480	0.01943	0.03516	0.00371
3	76° 49.3′	46° 52.6′	318° 38.2′	0.63989	0.85233	0.01073	0.01912	0.00234
4	79° 37.0′	47° 30.4′	U^a + 44° 10.0′	0.55557	0.77736	0.00680	0.01204	0.00157
5	81° 25.0′	47° 50.2′	U + 128° 47.6′	0.48982	0.70572	0.00469	0.00829	0.00110
6	82° 40.7′	48° 01.9′	U + 212° 54.8′	0.43751	0.64608	0.00344	0.00606	0.00082
7	83° 36.8′	48° 09.4′	U + 296° 43.2′	0.39504	0.59541	0.00263	0.00463	0.00063
8	84° 20.1′	48° 14.6′	2U + 20° 17.4′	0.35999	0.55131	0.00207	0.00365	0.00050
9	84° 54.6′	48° 18.2′	2U + 103° 45.2′	0.33209	0.51294	0.00169	0.00298	0.00041
10	85° 22.6′	48° 20.8′	2U + 187° 07.6′	0.30555	0.47945	0.00139	0.00244	0.00034
11	85° 45.9′	48° 22.8′	2U + 270° 24.6′	0.28372	0.44993	0.00117	0.00205	0.00028
12	86° 05.6′	48° 24.4′	2U + 353° 36.8′	0.26535	0.42371	0.00099	0.00174	0.00024
13	86° 22.5′	48° 25.7′	3U + 76° 45.4′	0.24888	0.40021	0.00085	0.00150	0.00021
14	86° 37.1′	48° 26.7′	3U + 159° 53.2′	0.23434	0.37922	0.00074	0.00131	0.00018
15	86° 49.8′	48° 27.5′	3U + 242° 59.6′	0.22150	0.36034	0.00065	0.00114	0.00016
16	87° 01.1′	48° 28.2′	3U + 326° 03.4′	0.20983	0.34304	0.00058	0.00102	0.00014
17	87° 11.1′	48° 28.8′	4U + 49° 05.4′	0.19939	0.32743	0.00052	0.00091	0.00013
18	87° 19.9′	48° 29.3′	4U + 132° 06.4′	0.09008	0.31334	0.00046	0.00081	0.00011
19	87° 28.0′	48° 29.7′	4U + 215° 08.0′	0.18138	0.30009	0.00042	0.00073	0.00010
20	87° 35.3′	48° 30.0′	4U + 298° 10.6′	0.17352	0.28800	0.00038	0.00067	0.00009

k	∊(ä)	ρ(ä)	ρ_s(ä)	ρ_p(ä)	I(k): ρ(ä)	I_s(k): ρ_s(ä)	I_p(k): p_p(ä)
1	20° 58.1′	0.02071	0.02507	0.01634	2.223	3.500	0.260
2	25° 34.5′	0.02100	0.02769	0.01433	0.926	1.270	0.260
3	69° 19.1′	0.12633	0.21003	0.04263	0.085	0.091	0.055
4	67° 55.0′	0.11141	0.19098	0.03184	0.061	0.063	0.049
5	25° 36.2′	0.02100	0.02772	0.01429	0.224	0.299	0.077
6	16° 27.4′	0.02057	0.02320	0.01794	0.167	0.261	0.046
7	58° 21.6′	0.05356	0.10485	0.00227	0.049	0.044	0.277
8	78° 51.3′	0.31038	0.41944	0.20132	0.0066	0.0087	0.0025
9	38° 07.4′	0.02446	0.04040	0.00853	0.069	0.074	0.048
10	03° 33.8′	0.02039	0.02053	0.02025	0.068	0.118	0.017
11	45° 12.3′	0.02820	0.05369	0.00272	0.041	0.038	0.104
12	86° 48.4′	0.70733	0.77709	0.63757	0.0014	0.0024	0.0004
13	51° 37.3′	0.03643	0.07273	0.00014	0.023	0.021	1.530
14	10° 03.4′	0.02049	0.02145	0.01953	0.036	0.061	0.0093
15	31° 29.8′	0.02181	0.03246	0.01116	0.030	0.035	0.014
16	72° 59.7′	0.17016	0.26697	0.07336	0.0034	0.0038	0.0019
17	65° 27.3′	0.09064	0.16224	0.01904	0.0057	0.0056	0.0066
18	23° 56.8′	0.02088	0.02668	0.01507	0.022	0.030	0.0076
19	17° 34.0′	0.02058	0.02359	0.01757	0.020	0.031	0.0058
20	59° 05.3′	0.05623	0.10938	0.00307	0.0067	0.0061	0.030

Abstract

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Figures (5)

Tables (2)

Applied Optics