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

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

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

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

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

Schlieren Photography

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.

Alcohol drop into water

Hydrogen gas from nozzle into air

Vortex from blade

5 joule spark under water

Ice cube floating in water

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.

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

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:

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

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

We define wave front as surfaces of constant phase

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 ?

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)

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

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

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

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

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

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

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

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  

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

Chile Jan 18 2017

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

Sunset blue flash, Christmas Eve, Paranal Observatory, Chile

Malibu CA, 24 min after sunset Feb 15 2014