[Tfug] Another OT Optics Question

Jeremy D Rogers jdrogers at optics.arizona.edu
Mon Aug 4 06:19:32 MST 2008


[snip]
>> 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.

>> 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.
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
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.

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

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.




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