[Tfug] Another OT Optics Question

[Hubert M Bath]

Bexley Hall wrote:
> OK, zero-th order understanding of how rainbows manifest
> themselves...  :>
> 
> Inceident ray comes back ~40 degrees refracted (and reflected).
> So, can I think of rainbow as a "conic section" in a cone with
> a 42 degree apex?

The 42 degrees applies to red light, and 40 degrees to violet, the 
inside of the "primary" rainbow. These angles apply no matter the height 
of the sun.  Only if the sun is at the horizon, and sun's rays therefore 
parallel to the earth's surface does the rainbow appear as a semicircle 
--with its center at the horizon.  If the sun is higher, the rainbow 
center is below the horizon and the rainbow less than a full semicircle. 
    If the sun is not so low, the rainbow moves down, so that its center 
is below the horizon, rather than at it.
> 
> And, the apparent "diameter" of the rainbow is a function
> of how far the water is from the observer?  E.g., a rainbow
> thrown from the mist of a gargen hose would appear to have a much
> smaller diameter than one from water vabor many miles distant.

I think that the *angular* diameter remains the same, tho, obviously, 
the actual refraction-reflection-refraction is occurring much closer 
than if the drops were from a distant rainstorm.  And, because the sun 
is presumably 'way above the horizon, the the arc of the spraybow would 
be less than a semicircle.  In fact, if the sun is more than 42 degrees 
above the horizon, a rainbow is impossible (because its "center" is more 
than 42 degrees below the horizon.)
> 
> (I'm not looking for "6 decimal places", here... just a crude
> understanding of the geometry involved  :>  )
> 
> Thx!
> --don
> 
> 
Regds,  Hu Bath