Announcements 10/31/12
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Prayer
Missing slinkies from: Seth, Ryan, William B, Mike P, Clement
Exam grading—will start right after class today, hopefully done by
tomorrow
Term project – progress report due Sat, Nov 10. Grading, out of
10 pts:
a. Did you submit a progress report on time?
b. Did your progress report show evidence that you had made
significant progress on your project, and that you were on
track to complete your project on time?
c. Was it less than 650 words and in the correct format (text in
body of email, partners CC’ed, figures as attachments if
needed)?
Pearls
Before
Swine
From warmup
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Extra time on?
a. (nothing in particular)
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Other comments?
a. These last few sections have been very fun.
b. This section wasn't as interesting for me as
others, so I'm in the mindset of "give me the
problems so I can get this section over with."
Clicker question (review answer):
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In polarized sunglasses, some of the glare
from the sun is eliminated when the sun is
directly in front (and above) you. Should the
polarizing material be aligned to allow vertical
or horizontal electric fields through?
a. vertical
b. horizontal
Brewster’s angle, review
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The Equation
1 
n2 
q1  tan  
 n1 
Why is 90 special?
“Brewster’s Angle”
p-polarization
field amplitudes vs q
1.0
t
0.8
0.6
0.4
r
0.2
20
0.2
40
60
80
What’s an image?
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When you look at it, it looks like there’s an object
present at a certain location (but there isn’t,
really)
Real
a. The light rays you see all pass through the
location of the image
Virtual
a. The light rays you see all just seem to be
coming from the location of the image
Clicker question:
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Is the image you see behind a mirror real or
virtual?
a. Real
b. Virtual
How can you ever get a real image to form with a mirror?
A Real Image
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Use a curved mirror
On the advantages of arrows…
From warmup
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What does it mean for a mirror to have a large
"radius of curvature"?
a. The mirror, while still curved, it quite flat. If
you were to extend it all the way, it would
make a gigantic sphere.
Clicker question:
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What is the focal length of a concave mirror with
a radius R?
a. R
b. -R
c. R/2
d. -R/2
e. R2
Proved in a HW problem
From warmup
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While decorating your Christmas tree you notice
that you can see yourself in one of the spherical,
reflective ornaments. Is your image real or
virtual? How do you know?
a. I think it's virtual. The rays of light aren't
actually passing through the point.
b. Virtual, because it appears to be inside the
ornament.
Demos
Saucer real image or not. Class poll: What kind of
image is this?
a. Real
b. Virtual
 Spherical mirror with hanging ball pendulum
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Curved mirrors
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Not just any curve will work
Fig 36.8
Fig 36.10
Focus:
a. every ray coming in parallel will pass through focus
b. every ray passing through focus will exit parallel
I will always use f, not R (f=R/2)
“paraxial rays”
Where will it “focus”?
focus
useful “third ray”:
center of mirror is flat
The equation
p
ho
hi
focus
f
q
Similar triangles:
hi q

ho p
Similar triangles:
hi
f

hi  ho p
The equation:
1 1 1
 
p q f
From warmup
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Will a converging (concave) mirror ever produce
a focused image at the focal point? If yes,
when? If not, why not?
a. Yes if light comes from an object infinitely far
away (so that incoming rays are parallel to the
plane of the mirror)
b. (My answer) No, because the object would
have to be infinitely far away
Magnification
p
ho
hi
focus
f
Similar triangles
hi q

ho p
hi
Define M: M 
ho
q
Useful way
q
to calculate: M  
Force M to be negative if image is inverted.
p
Demo
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Inverted image in light bulb
“Convex mirror”: curved the other way
The equation:
1 1 1
 
p q f
virtual image!
 but f is negative
Numbers: f = -5.5 cm, p = 16.5 cm, q = ? -4.1 cm
Negative q: means image is in back of mirror
Clicker question:
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Does a concave (converging) mirror always form a
real image?
a. Yes
b. No
Rest of time: class-designed problem(s)
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p = _____
f = _____
ray diagram = ?
q=?
M=?