| Chronology | Current Month | Current Thread | Current Date |
| [Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Carl Mungan
Sent: Tuesday, April 08, 2014 1:44 PM
To: phys-l@phys-l.org
Subject: [Phys-L] highway mirage
There seems to be a problem with typical textbook discussions of the
highway mirage of a pool of water appearing on a hot road. If the index n
monotonically decreases as we drop in altitude toward a hot road, shouldn't
a ray of light from the sky bend toward 90 degrees (so that it is traveling
parallel to the road)? What bends it upward?
One fix I have heard of is to say that once the ray gets close to being
horizontal, it reaches the critical angle and totally internally reflects off the
warmer layer of air below it.
Sounds good at first, but that explanation seems as flawed as the textbook
discussions on closer thought. The equation for critical angle is ArcSin[n2/n1].
If n2 = n1-dn, then the critical angle approaches 90 degrees as dn -> 0 for a
continuous function. There is no single well-defined critical angle unless you
have layers of air with steps in the index between them.
So who has a better fix? I suppose we could get small discontinuous steps
due to fluctuations.
Or perhaps one could say that even before it reaches the critical angle, more
and more of the light begins to reflect as the angle approaches 90 degrees.
Again this sounds reasonable, but I'd like to see it quantitatively checked
before I accept it. It should be experimentally testable, because it suggests
that a single incident ray will gradually reflect into a fan of rays.
Finally I suppose one could abandon ray optics and consider distortions of the
actual wavefronts.
Discussion?
--
Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F) Naval
Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/
_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l