1. Reading Quiz
I read the assignment for at least 20 min.
yes no

2. xxx http://en.wikipedia.org/wiki/Group_velocity

3. Reading Quiz
Who deduced the principle that says light rays moving from pt A to pt B will take the path that takes the least amount of time?
Faraday
Fraunhofer
Fresnel
Fourier
Fermat
Focoult
Feynmanns

4. Reading Quiz
The approximation made to derive the Eikonal equation (or to use rays in general) was ____
long wavelength regime
short wavelength regime

5. Announcements
I sent an about submitting questions for our exam review on Wed.
Exam 2 Thurs noon-Sat.

6. Schlieren Photography

8. Knife edge or filters makes image sensitive to x is  to edge
Knife edge or filters makes image sensitive to x is  to edge. Darker regions deflect some light onto the blade. Brighter regions deflect light that would normally hit the blade, past it.

12. Alcohol drop into water

14. Hydrogen gas from nozzle into air

17. Vortex from blade

18. 5 joule spark under water

19. Ice cube floating in water

20. Optical rays vs. waves
Rays are description of light energy flow (Poynting vector S), ignoring wave interference.
Applies best when l is _____ (k is ___)
Example: Snell’s law can predict “wave guiding” based just on n at interfaces.

21. What continuous equation do rays obey?
What if there is no interface? n varies continuously here:
What continuous equation do rays obey?

22. Assume
n can change with position, but not with direction of k or polarization of E.
2) significant changes in n must take place over many wavelengths:

23. One type of graded index (GRIN) rod has an index n(r) that increases outward from the center of the rod
A plane wave enters from the left. Draw surfaces of constant phase (how the planes and their spacings morph) inside the rod based on the speed of the waves, i.e. based on …what parts get ahead of others?
I got it mostly right
I tried but got it mostly wrong

24. Now draw rays, which are perpendicular to the surfaces of constant phase.
The effect of this rod is to _____ the light beam
converge
diverge

25. We define wave front as surfaces of constant phase

26. Surfaces of constant phase
We can write plane waves as
tells us the phase due to changes in position
are planes of constant phase.
What constant do we choose to get surfaces separated by ?

27. Surfaces of constant phase
spherical wave in spherically symmetric n(r)
To conserve power of wave:
The waves propagate perpendicular to surfaces of constant phase (contour surfaces)

28. Surfaces of constant phase
Find for a cylindrical wave
I got it mostly right
I got it mostly wrong, but tried
Find for a cylindrical wave that conserves power
I got it mostly right
I got it mostly wrong, but tried

29. A few key steps to the eikonal equation
Put into wave equation to
find equation for :
Approximation on l,k: _________
Eikonal equation

30. Eikonal Equation R (phase) changes most in space where n is large
Surfaces of constant phase are farther apart where
n is smaller
the wave moves faster
l is larger
Rays are paths perpendicular to contours (surfaces ) of

31. Comparing n-gradient effect to Snell’s law for layered glass
If n is largest at the top of this layered glass structure, what will the rays do?
turn downward
turn upward

32. Mirages
Rays leave the mountain top in all directions. On a hot day, which ray paths can go to her eyes?

33. Another form of Eikonal equation
s tells us where along a ray path we are.
gives us the direction of the ray.
If n changes reasonably slowly, the ray will turn toward the direction of ____________ n!
increasing

34. Fermat’s principle
Light rays traveling from point A to point B travel by the path(s) that…
minimize or maximize the time.

35. Sunset’s inverted mirage
Suppose the sun is actually below the horizon. You could possibly still see it if n _________ with height.
a) increased b) decreased

37. Surface heating, inversions
Atmosphere can have complicated function of n(h), including layers

38. Chile Jan

39. “Green flash” at sunset
Highest frequencies appear last. Can you explain this?

40. Sunset blue flash, Christmas Eve, Paranal Observatory, Chile

41. Malibu CA, 24 min after sunset Feb 15 2014