[Tfug] Another OT Optics Question

[Bexley Hall]

Hi, Jeremy,

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

> > To be clear... the rainbow *does* form a circular arc
> (?)
> > as a slice of that 40 degree cone  (?)  So, the
> farther
> > the observer iws from the phenomenon, the larger the
> > apparent radius becomes?
> 
> You're right, but I'd not say it's a slice of a
> cone in general. It

I think of it in these terms since the rainbow exists in a single
plane, right?  And, the water droplets in that plane are all
refracting the light back to me "bent" towards the center of
that "circle" at a ~40 degree angle -- my eyes being the
"focus" (apex).  So, the rays of light form a cone with the
rainbow occuring at a "slice" across that cone... (?)

(sorry, I'm just trying to relate this to things I understand! )

> really is just a circle or part of a circle. Perhaps a
> better way to
> think of it is that the light from visible wavelengths
> scatters from
> raindrops (refracts on the way in, reflects off the
> backside, refracts
> on the way out) at 30 degrees from the angle of incidence.
> Now that
> happens in a cone pattern for each and every raindrop. But,
> you don't
> see that cone, you only see one 'ray' from that
> cone because your eye
> is only at one point on that cone. However, there are lots
> of
> raindrops, so you can see any ray that reaches you eye from
> any

Yes.  I.e., if I step one step forward, I now am at
the apex of yet another "cone" whose rainbow is one foot
beyond the previous one (?).  I.e., no two rainbows are
really the *same* rainbow (unless you remain in a single
fixed position wrt the water mist)

> raindrop. Magically (actually geometrically), all those
> rays form
> another 40deg cone from your eye to the cloud.
> 
> > (sorry, this isn't my field so I need to take baby
> steps)
> >
> >> 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.)
> >
> > Oooh! This is an interesting observation!
> > But, are you sure of that?  I grew up in New England
> > pretty close to that 42 degree N line and I *know* I
> > saw rainbows as a kid (I am trying to remember if
> > I ever saw them in New Hampshire...)
> 
> Ah, Hu did not mean latitude. You could be at high

Ah, OK.

> latitudes or low
> latitudes, but if the angle straight from the sun down to
> the horizon
> is 40 degrees, the location of the center of the rainbow
> would be 40
> degrees below the horizon which means the top of the
> rainbow would be
> right at the horizon and you would not see it. Imagine

Understood.  Yes.

> it's noon at
> the equinox in Chicago (42deg), the sun is due south and
> 90-42=48 deg
> above the southern horizon. There is a rainstorm to the
> north, but the
> rainbow would be formed below the northern horizon with the
> center 48
> degrees below the northern horizon, and the top forming
> just 8 degrees
> below. If there are no raindrops between me and the ground
> (the storm
> is a ways off), I don't get to see the pretty colors.
> However, if I
> went up in a tall tower so that I look down at the rain
> cloud, I would
> be able to see it. Although it would be easier to just
> spray the hose
> in front of me while facing north.
> 
> Hope that's enlightening (hehe),
> JDR

Yes, thanks!
--don