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[Phys-l] Rainbows

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