Schlieren Photography

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.

n

x

n

x

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 (Poyting 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:

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

Surfaces of constant phase

We can write plane waves as

( ), vaci k r r t i k R r t

o oE r t E e E e

tells us the phase due to changes in position

vack R r

( )R r

constantvack R r

are surfaces of constant phase.

ˆ( ) kn r u r

What constant do I need for surfaces separated by ? r

What equation do rays obey?

spherical wave in spherically symmetric n(r) , vaci k R r t

oE r t E r e

In these examples, the waves propagate perpendicular to surfaces of constant phase (contour surfaces) constant

vack R r

( )R r

To conserve power of wave:

oE r

2

2o

o

n cI E

Surfaces of constant phase

, vaci k R r toE r t E r e

In all these, the waves propagate perpendicular to surfaces of constant phase (contour surfaces) constant

vack R r

Find for a cylindrical wavea) I got it mostly rightb) I got it mostly wrong, but tried

( ) ( , )R r R z

Find for a cylindrical wave that conserves powera) I got it mostly rightb) I got it mostly wrong, but tried

( )oE r f

A few key steps to the eikonal equation

Put into wave equation to

find equation for :

, vaci k R r toE r t E r e

R r 2

22 2

10

EE

c t

( )

2 2 2 0vac vac

vac

ik R r ik R r

o oE r e k n r E r e ( )

R r n r Eikonal equation

Approximation on l,k: _________

Surfaces of constant phase are farther apart where is _____________ a) larger b) smaller

Eikonal Equation

R r n r

n r

Rays are paths perpendicular to R r

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

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 rightb) I tried but got it mostly wrong

n r

Now draw rays perpendicular to the surfaces of constant phase.

The effect of this rod is to _____ the light beama) convergeb) diverge

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?

Mirages

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

s tells us where along a ray path we are. gives us the direction of the ray.

Another form of Eikonal equation

ˆR r n r s ˆd

ns nds

s

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

Atmospsere can have complicated function of n(h)

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

Sunset blue flash, Christmas Eve, Paranal Observatory, Chile

Malibu CA, 24 min after sunset Feb 15 2014