Details

= impact parameter

= angle for the -order rainbow

refraction indices for water:

red 1.3312

orange 1.3335

yellow 1.3342

green 1.3380

blue 1.3400

indigo 1.3415

violet 1.3435

Snapshot 1: the primary rainbow

Snapshot 2: the secondary rainbow

Snapshot 3: violet ray with three reflections

Snapshot 4: secondary rainbow for glass sphere

Snapshot 5: rays after two reflections in a water drop; no rainbow because intensity when

References

[1] J. D. Walker, "Multiple Rainbows from Single Drops of Water and Other Liquids," American Journal of Physics, 44(5), 1976 pp. 421–433. doi:10.1119/1.10172.

[2] R. L. Lee and P. Laven, "Visibility of Natural Tertiary Rainbows," Applied Optics, 50(28), 2011 pp. F152–F161. doi:10.1364/AO.50.00F152.

[3] M. Großmann, E. Schmidt and A. Haußmann, "Photographic Evidence for the Third-Order Rainbow," Applied Optics, 50(28), 2011 pp. F134–F141. doi:10.1364/AO.50.00F134.

[4] M. Theusner, "Photographic Observation of a Natural Fourth-Order Rainbow," Applied Optics, 50(28), 2011 pp. F129–F133. doi:10.1364/AO.50.00F129.

[5] H. E. Edens, "Photographic Observation of a Natural Fifth-Order Rainbow," Applied Optics, 54(4), 2015 pp. B26–B34. doi:10.1364/AO.54.000B26.

[6] D. T. Ivanov and S. N. Nikolov, "A New Way to Demonstrate the Rainbow," The Physics Teacher, 54(8), 2016 pp. 460–463. doi:10.1119/1.4965263.

[7] M. Welter, "Another Rainbow Demonstration with a Glass Sphere," The Physics Teacher, 57(5), 2019 p. 344. doi:10.1119/1.5098931.