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Re: [Phys-l] Rainbows

The most accurate and up to date analysis of "the Rainbow" is as Mie scattering.

An online calculator's second example includes the "rainbow angle(s)"*:

Home page:

Here's Wiki's page(s) on Mie scattering:

* bottom of the page:

This is the mother page:


"Numerical ray tracing by BowSim shows that departures from sphericity by a mere 1-2% noticeably distort the primary bow. We have to marvel that rainbows are ever seen!"

p.s. I get for the p polarization:

(Rp/Ep)^2 = (Tan(i - arcsin((n/n') sini)) / same w/ +)^2

A plot reveals very low reflection till 47 deg (15%) and the crit angle is ~ 49 deg.

the p wave begins at ~ 14%, and is ~ 40% at 40 deg.

Robert Cohen wrote:

In this month's "The Physics Teacher", there is a letter to the editor
regarding the reflection of light in the rainbow. In the letter, the
writer makes two arguments that I can't seem to make sense of.

1. The writer argues that the primary rainbow is 2% as bright as the
light incident upon the raindrop because the internal reflection is
proportional to the square of the difference of the indexes. Is this
true? Shouldn't this depend on the incident angle?

2. The writer argues that if the light were totally internally
reflected, the primary rainbow (as well as the secondary rainbow and all
higher-order rainbows) would be as bright or intense as the light
incident on the water drop. Is this true? Wouldn't this assume that
the raindrops intercept all of the light (no light gets through), no
light reflects off the raindrops, and all of the light incident upon the
raindrop is refracted the same amount and experiences TIR? How could
all the rainbows be equally intense?

Primary point of the letter was to point out that the internal
reflection is not total and I have no problem with that (although it
isn't clear to me if this is the case for all incident angles); I just
have difficulty following the two arguments above.

Robert A. Cohen, Department of Physics, East Stroudsburg University 570.422.3428
Forum for Physics Educators