Transcript lecture 31 - magnifier, telescope

Announcements 11/7/12
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Prayer
Term project progress report due Saturday night
a. Evidence of progress
b. Text in body of email, list of group members,
and group members CC’ed on the email
Calvin &
Hobbes
From warmup
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Extra time on?
(nothing)
Other comments?
a. What does “subtends” mean? (2 people)
Clicker quiz
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Have you tried LearnSmart?
a.yes
b.no
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If you have tried it, how useful has it been? (only
answer if you have tried it)
a.Very
b.Moderate
c. Slightly
d.Not at all
Summary of Near point vs. Far point
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Person A = nearsighted
a. Can’t focus on object at infinity
b. Use lens to bring object at infinite to image at
“far point”
– image distance = negative!
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Person B = farsighted
a. Can’t focus on object at 25 cm (comfortable
reading distance)
b. Use lens to bring object at 25 cm to image at
“near point”
– image distance = negative!
From warmup:
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Compare the two situations: (1) You are using a
magnifying glass to start a fire by focusing the sun's
rays onto some straw. (2) You are using a magnifying
glass to help you read small print. Qualitatively, what
would "p" be for each situation? What would "q" be?
a. 1)p is the distance to the sun from the magnifying
glass, q is the distance of the magnifying glass to the
straw
2)p is the distance from the letters to the magnifying
glass, q is the distance of the magnifying glass to
your eye
Very common answer, but wrong!
Quick writing: what is q for case 2? (talk to your
neighbors; click in when you’re ready to answer)
From warmup:
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Which will look bigger* to you, a 1 m tall object
that’s 5 meters away from you, or a 10 m tall
image that’s 50 meters away from you?
a. They will look the same size. They both are at
an angle of arctan(5/1) with respect to the
principal axis.
*
In the sense that it takes up more of your field of view
“angular size”
Worked Problem
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What is the angular size of a 0.1 m tall object
that’s 5 meters away from you?
Two methods!
Thought Question
 Which method should you use?
a. Method A
b. Method B
Quick writing
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You are looking at an ant, h = 1 mm. What
is the maximum viewing angle you can use
to look at the ant, without any lenses?
“Colton picture”
r
q
q (in radians) = (section of arc)/r
Clicker question:
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Which of the following is NOT true of angular magnification?
a. It is more useful than the absolute magnification when
discussing telescopes
b. It is more useful than the abs. magnification when
discussing magnifying glasses
c. It is given by the equation m = -q/p
d. It is likely to show up on an exam.
m = q/q0 … where q0 = “the best you can
do without magnification”
Magnifying Glass
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The setup:
f = 10 cm
Where would you like the image to be?
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Let’s pick q = -50 cm. (q would generally be given in
problem.)
Answers:
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What is m? (m = q/q0)
q = 6h/50 rad
a. What is q?
q0 = h/25 rad
b. What is q0?
m=3
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Note: using formulas from book…
mmax = 3.5 (for q = 25 cm)
mmin = 2.5 (for q = infinity)
Quick writing
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You are looking at the planet Mars, “h”
(diameter, really) = 3.4  106 m. The planet,
as you are looking at it, is 2.5  1011 m away
(this changes from month to month based on
the relative positions of Mars and Earth).
What is the maximum viewing angle you can
use to look at Mars, without any lenses?
“Colton picture”
r
q
q (in radians) = (section of arc)/r
Telescope
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The setup:
Given details of
setup, what is m?
(m = q/q0)
a. What is q0?
b. What is q?
These focal spots should essentially
overlap (not shown properly in this figure)
“Colton picture” for q
r
Answers:
q0 = h/r
q = foh/(rfe)
m = fo/fe
fo
Because Mars is so far away, image is
formed at the focal spot (essentially)
Height of image = hfo/r
fe
(from M = -q/p)
triangle: q (rad) =
(intermed. height)/fe
q
image
If intermediate image were formed exactly at the
focal point of the eyepiece, final image would be
at . As it is, it will just be very far away.
Regardless of how far away it is, though,
the angle is given by the blue ray.
From warmup
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Compare these two Wikipedia lists: Largest optical
reflecting telescopes and Largest optical refracting
telescopes. Which list contains the largest
telescopes overall, and why are the largest
telescopes all that variety?
a. Reflecting is much larger. The glass in large
refracting telescopes would sag so they use
mirrors instead since they can support the back
of them.
b. reflecting telescopes are larger. this is because
there are no aberration issues with reflecting
telescopes so they can give clearer images.
c. Also (my answer): only need to polish one side—
saves a lot of money
Reflecting Telescope
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A “Newtonian Reflector”
eyepiece lens
Incoming
Light
Curved
Mirror
Mirror
http://lcogt.net/en/book/reflecting-telescopes
Compound Microscope
I really dislike the eqn:
“overall magnification” =
Mobjective  meyepiece
because it mixes absolute
magnification with angular
magnification
(but apparently everyone does it
that way)
 Not on reading assignment, not
on HW, not on exam, not especially
interesting… let’s not bother with.
Onward!
http://en.wikipedia.org/wiki/Microscope
Chapter 37!
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Interference effects
a. I.e. now returning to wave nature of light,
instead of the ray approximation
Two mathematical facts we will use:
e e
cos x 
2
ix
ix
e e
sin x 
2i
ix
ix
Interference...
A single source
Next few slides: credit Dr. Durfee
Interference...
Two sources