Re: OT raibow

[A complimentary Cc of this posting was sent to
Joost Diepenmaat
<joost@xxxxxxxxx>], who wrote in article <475203a8$0$20387$e4fe514c@xxxxxxxxxxxxxxxxxxxxxxxx>:
On Sun, 02 Dec 2007 00:35:53 +0000, Ilya Zakharevich wrote:
A rainbow contains VERY mixed colors. It's a wonder that these colors
are distinguishable by eye at all; they are very low saturation (even if
the background is very dark - which it usually is not).

Getting further and further off-topic.

I am under the impression that a rainbow contains/is a "frequency sweep"
of visible light, which would mean that the colors aren't mixed - at
every point you'd have light of a single frequency.

It is very very far from being true. Looking at the picture of ray
tracing through a droplet, you can see that there is A CONCENTRATION
of rays going out near a certain cone; as with "the usual `fold'
concentrators" (see catastrophe theory) the corresponding density will
be about const/sqrt(A-a0); here A is the angle with the direction to the
sun, and a0 the angle at the vertex of the cone. a0 depends slightly
on the frequency of light.

Therefore, looking in the particular direction A, you get density of
rainbow light with frequency F as const/sqrt(A - a0(F)); this may be
rewritten as something "about const/sqrt(F - F0)". "Single frequency"
conjecture corresponds to distribution with density concentrated at
one particular frequency F0.

Since dependence of a0 on F is very small, this "about" above should
give quite good an approximation; thus the distribution is "very
wide", not "very narrow".

Hope this helps,
Ilya
.

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