[Tfug] Another OT Optics Question

[Bexley Hall]

Hi, Jeremy,

--- On Sun, 8/3/08, Jeremy D Rogers <jdrogers at optics.arizona.edu> wrote:

> >> 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 think Hu's right, but just to be clear, if the
> 'angular' size is
> always ~40deg, then it always appears the same size.

Sorry, I don't understand this comment.  A rainbow
from my garden hose "appears" 5 or ten feet in diameter.
It *never* appears as large as one that I see in the distance

> Looking at a
> rainbow formed by the mist of your garden hose (which could
> be a full
> circle since the mist can be between you and the horizon),
> you might
> be fooled into thinking it looks smaller because the stuff
> next to it
> is closer, but in terms of angles, it's the same.

If I hold my hands 2 feet apart and one foot in front of my
eyes, I can line them up with two buildings down the street.
Yet, I *know* those two buildings are much farther apart than
2 feet!  :>

I.e., if I could "see" where the distant rainbow met the ground
at each of its extremities, I would *know* that those two
points are much farther apart than the 5-10 feet from my
garden hose rainbow!  Despite being "similar triangles", etc.

So, I know the garden hose rainbow is N feet from me and 5 feet
wide.  If I had a yardstick on the horizon, I could take the
rainbow's extremities, divide by 5 and "know" that the rainbow
was (X/5)*N feet from me...

RIght?
 
> >> (I'm not looking for "6 decimal
> places", here... just a crude
> >> understanding of the geometry involved  :>  )