Double Rainbows in Princeton
It is fall, and the trees are glowing.
I'm glad I'm teaching 205 Lagrangian mechanics, not just because the students are great, but because I learned how rainbows are formed, properly! For 26 years (ok, less) I have cultivated this picture of a beam of light entering a droplet and dispersing, ala Wikipedia illustration. I got a huge kick from discovering, through calculation, that this is wrong. The reason is that each wavelength really has a different critical impact parameter! A rainbow forms when there is constructive interference: the derivative of the scattering angle with respect to the impact parameter vanishes. Depending on the wavelength, this quantity vanishes for different impact parameters.
A typical rainbow is formed by the third scattering: light enters the droplet, reflects once, and leaves the droplet. A double rainbow sometimes forms from a fourth scattering (which explains how fragile it looks), and with the opposite negative parameter (which explains why the colors run in the opposite direction). This is in contradistinction (love this word, thank you Landau's translator) to Wikipedia's picture, which would predict that the colors flip direction with every reflection, independent of the impact parameter. I must tell people about this wonderful news. I feel like Fake Russian.
I'm glad I'm teaching 205 Lagrangian mechanics, not just because the students are great, but because I learned how rainbows are formed, properly! For 26 years (ok, less) I have cultivated this picture of a beam of light entering a droplet and dispersing, ala Wikipedia illustration. I got a huge kick from discovering, through calculation, that this is wrong. The reason is that each wavelength really has a different critical impact parameter! A rainbow forms when there is constructive interference: the derivative of the scattering angle with respect to the impact parameter vanishes. Depending on the wavelength, this quantity vanishes for different impact parameters.
A typical rainbow is formed by the third scattering: light enters the droplet, reflects once, and leaves the droplet. A double rainbow sometimes forms from a fourth scattering (which explains how fragile it looks), and with the opposite negative parameter (which explains why the colors run in the opposite direction). This is in contradistinction (love this word, thank you Landau's translator) to Wikipedia's picture, which would predict that the colors flip direction with every reflection, independent of the impact parameter. I must tell people about this wonderful news. I feel like Fake Russian.
posted by Dr. Broke at 11:08 PM
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