Rainbows of Different Order in Water Droplets and Glass Beads

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A single reflection of sunlight inside a falling raindrop produces the primary rainbow. Double reflection gives rise to the secondary rainbow. This Demonstration calculates the parameters for rainbows of the first six orders. You can follow the rays as they are refracted and reflected in water droplets and glass beads to form rainbows of different order. You can move the relative position of the white light source using the locator.

Contributed by: Volodymyr Holovatsky and Elizabeth Orynchuk (August 2022)
(Yuriy Fedkovych Chernivtsi National University, Ukraine, and Vyzhnytsia Gymnasium, Ukraine)
Open content licensed under CC BY-NC-SA



= 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


[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.

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