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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