schlieren photography. knife edge or filters makes image sensitive to x is to edge. darker regions...
TRANSCRIPT
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Schlieren Photography
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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
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Alcohol drop into
water
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Hydrogen gas from
nozzle into air
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Vortex from blade
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5 joule spark under water
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Ice cube floating in water
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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.
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What continuous equation do rays obey?
What if there is no interface? n varies continuously here:
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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
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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
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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
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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
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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: _________
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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
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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
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Now draw rays perpendicular to the surfaces of constant phase.
The effect of this rod is to _____ the light beama) convergeb) diverge
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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?
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Mirages
Rays leave the mountain top in all directions. On a hot day, which ray paths can go to her eyes?
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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
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Fermat’s principle
Light rays traveling from point A to point B travel by the path(s) that…
minimize or maximize the time.
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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
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Surface heating, inversions
Atmospsere can have complicated function of n(h)
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“Green flash” at sunsetHighest frequencies appear last. Can you explain this?
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Sunset blue flash, Christmas Eve, Paranal Observatory, Chile
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Malibu CA, 24 min after sunset Feb 15 2014