explain WHY waves
refract
(bend)
as they go from one medium to another.
apply
refraction
of light to mirages.
apply
refraction
to
total internal reflection
and
fiber optics
.
I can . . .
use
Snell’s Law
and
Index of Refraction
to predict
the angle a ray of light will
refract
.
predict the direction a ray will
refract
based on the
http://tractortestlab.unl.edu/oldsite/cat/Cat75E.JPG
http://230nsc1.phy-astr.gsu.edu/hbase/sound/refrac.html#c1
Concrete Sand
Water Wave
http://7art-screensavers.com/screenshots/Wave/attracting-wave.jpg
The bottom of the wave “drags”
52,000 ft
$825/ft in ocean
$825/ft in ocean
$585/ft on land
$585/ft on land
15
,0
00
f
t
x
x
52,000 - x
52,000 - x
√1
5,
00
0
2
+
x
2
√1
5,
00
0
2
+
x
2
Cost = 825
Cost = 825
√15,000
2
+ x
2
√15,000
2
+ x
2
+
+
585(52,000 –x)
585(52,000 –x)
0
10000
20000
30000
40000
50000
60000
$36,000,000.00
$37,000,000.00
$38,000,000.00
$39,000,000.00
$40,000,000.00
$41,000,000.00
$42,000,000.00
$43,000,000.00
$44,000,000.00
$45,000,000.00
$46,000,000.00
Value of "X" (feet)
C
O
ST
($
199 861 638 m/s
Glass
225 407 863 m/s
Water
228 849 204 m/s
Ice
299 702 547 m/s
Air
299 792 458 m/s
Vacuum
Speed of Light
in Medium
Medium
Diamond
123 932 393 m/s
Index of Refraction =
speed
vacuum
speed
medium
Water
n
n
Index of refraction of Water
n
water
=
225,000,000
300,000,000
http://www.shokabo.co.jp/sp_e/optical/labo/refref/refr1.gif
Which medium does the wave travel slowest?
Air – “fast”
Concrete (Fast)
Deriving Snell’s Law
Medium 1
Medium 2
q
1
q
1
q
2
q
2
Consider two light
rays. Velocities are
v
1
in medium 1
and
v
2
in med. 2.
Segment
R
is common hypotenuse to two rgt.
triangles. Verify shown angles from geometry.
v
1
v
1
t
v
2
v
2
t
R
q
1
q
2
=
c/n
1
c/n
2
sin
θ
1
sin
θ
2
n
2
n
1
=
1
2
1
2
sin
v t
; sin
v t
R
R
q
q
1
1
1
2
2
2
sin
sin
v t
v
R
v t
v
R
q
Index
of Refraction =
speed
vacuum
speed
medium
Water
σ
2
σ
1
Air
Willebrord van Roijen Snell
1580-1626
n
air
·sin(σ
air
) = n
water
·sin(σ
water
)
Water
n
Air – “fast”
Water – “slow”
Air – “fast”
http://www.specialweb.com/photos/water/stream_bedb.jpg
http://www.darylscience.com/Demos/InvisibleTT.html
Corn Oil
Corn Oil
Air
http://cdn.phys.org/newman/gfx/news/2011/bendinglight.jpg
http://www.rp-photonics.com/img/negative_refraction.png
The boundary from one medium
to another is definitive.
http://sol.sci.uop.edu/~jfalward/wavessound/wavessound.html
http://sol.sci.uop.edu/~jfalward/wavessound/wavessound.html
Velocity
sound
= 330 m/s @ 0°C
(It increases by 0.6 m/s for every degree above 0°C.)
Cool Air (slow)
Warm Air (fast)
Cool Air (slow)
299 702 547 m/s
Air
299 792 458 m/s
Vacuum
http://www.greatestplaces.org/mirage/desert1.html
Photos by Pekka Parviainen
Flying Dutchman
http://www.wdtv.com/weather/images/Weather_Review/sky_optics_and_observations.htm
http://www.nasa.gov/centers/goddard/images/content/163786main_golfball_elnino_nov9_sm.jpg
When the effect appears above the water, it is often referred to as a
Fata
Morgana
. The phrase comes from the Italian version of the name of the
sorceress Morgan Le Fay from the legends of King Arthur and Camelot. In
ancient times these strange effects were considered the work of witchcraft.
Air – “fast”
Water – “slow”
Critical
Angle
n
1
·sin(σ
1
) = n
2
·sin(σ
2
)
n
water
·sin(
?
) = n
air
·sin(90)
n =
v
c
n
diamond
·sin(σ
1
) = n
air
·sin(σ
2
)
n =
v
c
·sin(
?
) = ·sin(90)
299,792,458
123, 932,393
299,792,458
299, 702,547
?
= 24.4
°
http://www.diamondocean.com/news/images/20071015_114_1.jpg
$15 Million 84 Carat Diamond Up For Auction!
Air – “fast”
Water – “slow”
Air – “fast”
Water – “slow”
http://www.shokabo.co.jp/sp_e/optical/labo/refref/refx1.gif
Air – “fast”
Water – “slow”
LAB – Index of Refraction
n
acrylic
= 1.49
θ
c
= 41.8°
?= 27.9°
1) Use a Graph to find
the
speed of light
in a
given rectangular
piece of material
Use at least 8 different data points.
2) Use the table to
determine what
material piece is
made of.
PURPOSE
Material
Index of
Refraction, n.
Fused Silica
1.46
Pyrex Glass
1.47
Plexiglas
1.49
Polycast Acrylic
1.49
High Density Polyethylene
(HDPE)
1.53
Poly Vinyl Chroride (PVC)
1.54
Angle o
f Incide
nce
Angle of Refra
ction
?
θ
c
n
acrylic
= 1.5
θ
c
= 41.8°
?= 27.9°
What angle of incidence would produce the critical angle
on the opposite face of the equilateral triangle?
