[Tfug] Another OT Optics Question

[Bexley Hall]

Hi, Jeremy,

--- On Mon, 8/4/08, Jeremy D Rogers <jdrogers at optics.arizona.edu> wrote:

> >> 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
> 
> True, it appears larger because although the angle is the
> same, you
> think it's farther away. So you interpret it as a
> larger diameter.

What do you mean, "think its farther away"?  *Isn't* it,
in fact, farther away?  (by "it", I mean the plane of water
droplets that are refracting the light, thus)
 
> >> 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?
> 
> Definately right. The reason I said it is the same in terms
> of angles,
> is that the rainbow really has no diameter.

Grrrr... this is bordering on the metaphysical!  :-/

OK, let's assume the rainbow is a real thing and not just
an optical manifestation.  Let's assume my point of observation
is fixed -- therefore, I have "fixed" the rainbow's "location"
(again, by rainbow, I mean the water droplets that are
refracting the light to me).

If I could freeze time/space and physically vacuum up all of the
water molecules that were NOT contributing to this perception
and then flash freeze all of those that remained, wouldn't I
end up with a *physical* "ice structure" having real dimensions
(that I could measure)?

> In Paul's comment, the moon appears larger near the
> horizon because
> you have objects to compare it with. I think that's
> kind of the same

I don't see it this way.  And, the geometry (the model that
I am clinging to) claims otherwise, also.  I.e., the water
vapor *is* farther away so the particular water molecules
that are refracting the light that *I* am perceiving as
a rainbow are farther physically apart (the "pots of gold",
so to speak).

I.e., the farther a rainbow is away from you, the "higher"
in the atmosphere the water vapor must exist for the
rainbow to be a complete arc (without the top of the
ARCH disappearing).

If the arc is taller, then it must also be wider (physically)

> thing, but if you physically walked (flew) closer to the
> moon, it's
> angular size would get bigger because it has a fixed
> diameter, and the
> angular size depends on your distance.

Undestood.
 
> However, if there is a rainstorm 1 mile away creating a
> rainbow and
> you walk half a mile towards it, the angular size stays the
> same. What
> happens is the actual raindrops reflecting light to you are
> the
> raindrops on a circle of diameter 2*0.7 miles. When you
> walk closer,
> it's a different set of raindrops reflecting light to
> you on a smaller

But that is no longer the same rainbow!

> circle. So the way I look at it, there rainbow doesn't
> have a physical
> diameter, only an angular extent.

OK, I think I follow you.
 
> But what you said is right, if you know the distance to the
> droplets
> (which is hard for a rainstorm above the horizon), you
> could calculate
> the diameter of the circle of raindrops forming your
> rainbow. But
> someone standing a little closer seeing the 'same'
> rainbow, is seeing
> light reflected from a different set of raindrops that are
> closer
> together.
> 
> I hope that helps. I feel like there is a clearer way to
> say this, but
> I'm not finding it.

"Tastes like milk..."

Thanks for your time!