1. Schlieren Photography

3. 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.

7. Alcohol drop into water

9. Hydrogen gas from nozzle into air

12. Vortex from blade

13. 5 joule spark under water

14. Ice cube floating in water

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

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

17. Assume 1) n can change with position, but not direction of k or polarization of E. 2) significant changes in n must take place over many wavelengths

18. Surfaces of constant phase We can write plane waves as tells us the phase due to changes in position are surfaces of constant phase. What constant do I need for surfaces separated by ?

19. What equation do rays obey? spherical wave in spherically symmetric n(r) In these examples, the waves propagate perpendicular to surfaces of constant phase (contour surfaces) To conserve power of wave:

20. Surfaces of constant phase In all these, the waves propagate perpendicular to surfaces of constant phase (contour surfaces) Find for a cylindrical wave a)I got it mostly right b)I got it mostly wrong, but tried Find for a cylindrical wave that conserves power a)I got it mostly right b)I got it mostly wrong, but tried

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

22. Surfaces of constant phase are farther apart where is _____________ a) larger b) smaller Eikonal Equation Rays are paths perpendicular to R 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

23. A particular graded index (GRIN) rod has an index n(r) that increases outward from the center of the rod Draw surfaces of constant phase inside the rod for a plane wave coming from the left that change when in the rod, based on the speed of the waves, i.e. based on a)I got it mostly right b)I tried but got it mostly wrong

24. Now draw rays perpendicular to the surfaces of constant phase. The effect of this rod is to _____ the light beam a)converge b)diverge

25. 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?

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

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

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

29. 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

31. Surface heating, inversions Atmospsere can have complicated function of n(h)

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

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

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