Unformatted text preview: Physics 212
Lecture 25 50
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Avg = 3.0 Confident Physics 212 Lecture 25, Slide 1 Music
Who is the Artist?
A)
B)
C)
D)
E) Miles Davis
Oscar Peterson
Gerry Mulligan
John Coltrane
Stan Getz Why?
Just in a classic jazz mood, I guess
I also was at a concert last Saturday when the
also
vocalist called Lush Life “obscure” hardly…… Physics 212 Lecture 25, Slide 2 Physics 212
Lecture 25 50
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Avg = 3.0 Confident Physics 212 Lecture 25, Slide 3 Let’s start with a summary: from n2 to n1
Physics 212 Lecture 25, Slide 4 The speed of light in a medium
The
is slower than in empty space:
is since ε0 > ε vmedium = c / nmedium
Physics 212 Lecture 25, Slide 5 Preflight 2
BB A
B
C
What about the wave must be the same on either side ???
60 Observers in both media must
agree on the frequency of
vibration of the molecules 50
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0 Physics 212 Lecture 25, Slide 6 Reflection Physics 212 Lecture 25, Slide 7 Refraction: Snell’s Law Physics 212 Lecture 25, Slide 8 Think of a day at the beach…
What's the fastest path to the ball knowing
you can run faster than you can swim? This one is better
Not the quickest route… Physics 212 Lecture 25, Slide 9 A x1
l1 y1 y2 l2
x2 B 1
Time from A to B = t = l1/v1 + l2/v2 =
Time
v1
dt
x1
x2
dx2
=
+
2
2
2
2
dx1 v1 x1 + y1 v2 x2 + y2 dx1 1
l1 x1
x
=2
v1l1 v2l2 1
x +y +
v2
2
1 2
1 2
2
x2 + y2 dt
x1
x2
=0=
−
dx1
v1l1 v2l2 l2 sin θ1 sin θ 2
=
v1
v2 n1 sin θ1 = n2 sin θ 2 Physics 212 Lecture 25, Slide 10
10 Preflight 6 80 Snell’s Law:
n1sinθ1 = n2sinθ2 60
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20 n decreases ﬂ θ increases 0 Physics 212 Lecture 25, Slide 11
11 Total Internal Reflection θ1 > θc
Simulation Total Internal Reflection
Physics 212 Lecture 25, Slide 12
12 Preflight 8 70
60
50
40 θc clearly depends on both n2 and n1 30
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13 Intensity Anything looks like a mirror
if light is just glancing off it. If two materials have the same n
then its hard to tell them apart.
Physics 212 Lecture 25, Slide 14
14 Preflight 4 70
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15 Polarization sin θ 2 = sin(90 − θ1 ) = cosθ1
n2
tan θ1 =
Snell’s Law: n2 sin θ 2 = n2 cosθ1 = n1 sin θ1
n1 θ1 + θ 2 = 90 Physics 212 Lecture 25, Slide 16
16 A ball sits in the bottom of an otherwise empty tub at the
ball
front of the room.
front
Suppose N people sit high enough to see the ball (N = ). Physics 212 Lecture 25, Slide 17
17 A ball sits in the bottom of an otherwise empty tub at the front of the room.
Suppose N people sit high enough to see the ball (N =
). Suppose I fill the tub with water but the ball doesn’t move.
Will more or less people see the ball? BB A) More people will see the ball
B) Same # will see the ball
C) Less people will see the ball θA
θw no wat ?? er water Snell’s Law: ray bent away from normal going from water to air
Physics 212 Lecture 25, Slide 18
18 Preflight 10
BB The light would go out in all directions, so only
some of it would be internally reflected. The
person would see the light that escaped after
being refracted. 70
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50
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30 DRAW SOME RAYS 20
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0 Physics 212 Lecture 25, Slide 19
19 Example: Refraction at water/air interface
• Diver’s illusion 97º Diver sees all of horizon
refracted into a 97°cone θ1 = 90 n1
n1
1
sin θ 2 = sin 90 = =
n2
n2 1.33 θ 2 = 48.5
Physics 212 Lecture 25, Slide 20
20 Exercise
A meter stick lies at the bottom of a
rectangular water tank of height 50cm.
rectangular
You look into the tank at an angle of
45o relative to vertical along a line that
45 relative
skims the top edge of the tank.
What is the smallest number on the
ruler that you can see?
ruler 45o nwater = 1.33
50 cm 0 20 40 60 80 100 Conceptual Analysis:
 Light is refracted at the surface of the water
Strategy:
 Determine the angle of refraction in the water
and extrapolate this to the bottom of the tank. Physics 212 Lecture 25, Slide 21
21 45o Exercise
A meter stick lies at the bottom of a
rectangular water tank of height 50cm.
rectangular
You look into the tank at an angle of
45o relative to vertical along a line that
45 relative
skims the top edge of the tank.
What is the smallest number on the
ruler that you can see?
ruler nwater = 1.33
50 cm 0 20 40 60 80 100 If you shine a laser into the tank at an angle of 45o, what is the
refracted angle θR in the water ?
A) θR = 28.3o B) θR = 32.1o C) θR = 38.7o BB Snell’s Law: nairsin(45) = nwatersin(θR)
sin(θR) = nairsin(45)/nwater = 0.532
θR = sin1(0.532) = 32.1o
Physics 212 Lecture 25, Slide 22
22 45o Exercise
A meter stick lies at the bottom of a
rectangular water tank of height 50cm.
rectangular
You look into the tank at an angle of
45o relative to vertical along a line that
45 relative
skims the top edge of the tank.
What is the smallest number on the
ruler that you can see?
ruler nwater = 1.33 θR 50 cm 0 20 40 d 60 80 100 θR = 32.1o What number on the ruler does the laser beam hit ? A) 31.4 cm B) 37.6 cm C) 44.1 cm BB tan(θR) = d/50
d = tan(32.1) x 50cm = 31.4cm Physics 212 Lecture 25, Slide 23
23 45o FollowUp
Follow
A meter stick lies at the bottom of a
rectangular water tank of height 50cm.
rectangular
You look into the tank at an angle of
45o relative to vertical along a line that
45 relative
skims the top edge of the tank. 50 cm nwater = 1.33 0 20 40 60 80 100 If the tank were half full of water, what number would the laser hit?
(When full, it hit at 31.4 cm)
A) 25 cm B) 31.4 cm C) 32.0 cm D) 40.7 cm E) 44.2 cm BB Physics 212 Lecture 25, Slide 24
24 45o 45o nwater = 1.33 θR 50 cm 50 cm
d = 50 cm d = 31.4 cm
0 20 40 60 80 100 0 20 40 60 80 100 θR = 32.1o
45o 50 cm nwater = 1.33 θR
0 20 d = 40.7 cm
40 25 cm + (31.4/2) cm 60 80 100
Physics 212 Lecture 25, Slide 25
25 More Practice
A monochromatic ray enters a slab with n1 = 1.5 at an angle θb as shown
θb
n=1 TOP n1 = 1.5
BOTTOM θb n=1 BB (A) Total internal reflection at the top occurs for all angles θb, such that sinθb < 2/3 (B) Total internal reflection at the top occurs for all angles θb, such that sinθb > 2/3 (C) There is no angle θb (0 < θb < 90o) such that total internal reflection occurs at top. Snell’s law: n1 sin θ1 = n2 sin θ 2 nsinθ is “conserved” Ray exits to air with same
angle as it entered !! Physics 212 Lecture 25, Slide 26
26 FollowUp
A ray of light moves through a medium with index of refraction n1 and is incident
upon a second material (n2) at angle θ1 as shown. This ray is then totally reflected
at the interface with a third material (n3). Which statement must be true?
θ1
n1
n2 (A) n3 < n1 (B) n1 < n3 ≤ n2 (C) n3 ≥ n2 n3
θ1 If n1 = n3 n1
n2
n3 Want larger angle of refraction in n3 BB θ1 n3 < n1
Physics 212 Lecture 25, Slide 27
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Full Document
 Fall '10
 Selig
 Physics, Snell's Law, refractive index, Total internal reflection

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