Re: [Phys-l] Rainbows

[Bernard Cleyet <bernardcleyet@redshift.com>]

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)"*:

http://www.lightscattering.de/MieCalc/quickstart1.html

Home page:

http://www.lightscattering.de/MieCalc/

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

http://en.wikipedia.org/wiki/Mie_scattering

* bottom of the page:

http://www.lightscattering.de/MieCalc/quickstart1.html


This is the mother page:

http://en.wikipedia.org/wiki/Rainbow

bc

"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!"

http://www.sundog.clara.co.uk/rainbows/twin1.htm


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   rcohen@po-box.esu.edu    http://www.esu.edu/~bbq
> _______________________________________________
> Forum for Physics Educators
> Phys-l@carnot.physics.buffalo.edu
> https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
>
>
>