Physics5 123A Waves and Modern Physics

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Physics5 123A Waves and Modern Physics
Lecture 11 (TM 32.3-4)Optical Images and
Instruments October 28, 2009 (23 Slides)

• John G. Cramer
• Professor of Physics
• B451 PAB
• cramer_at_phys.washington.edu

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Exam 1 Statistics
Average 64.8 Std Dev 14.2
High 100 Median 65 Low 10
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Lecture 11 Announcements

• Lecture Homework 4 has been posted on the
  WebAssign system. It is due at 1159 PM on
  Friday, October 30.
• Check your Exam 1 scores on WebAssign. If a 0
  is recorded, it may mean that we have not
  identified your paper.
• We will have Exam 2 on November 13. There will
  be assigned seating. If you want a left-handed
  aisle seat, a right-handed aisle seat, or a seat
  near the front, of if you require one of the four
  table seats in the back, send me E-mail with your
  request.
• So far 180/196 students have registered their
  clickers. A clicker response that shows up as a
  number may indicate a registration problem.

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Lecture Schedule (Part 2)
We are here!
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Snells Law
The Dutch physicist and mathematician
Willebrord Snell of the University of Leiden in
1621 discovered the law of refraction, also
called Snells Law.
In a medium in which light slows down, a ray
bends closer to the perpendicular.
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Refractive Surfaces Imaging
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Example Image Seen from a Goldfish Bowl
Goldie sees Fluffys image fartherfrom the
bowl than Fluffy actually is. Goldie the goldfish
is in a 15.0-cmradius spherical bowl of water
withnw 1.33. Fluffy the cat is sitting onthe
table with her nose 10.0 cm fromthe surface of
the bowl. The light from Fluffys nose is
refracted by the airwater boundary to form an
image. Find (a) the image distance and (b) the
magnification of the image of Fluffys nose.
Neglect any effect of the bowls thin glass wall.
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Thin Lenses
(fgt0)
When parallel rays pass through a diverging
lens, the rays diverge away from the focal point
f of the lens, and must be extrapolated back to
find it. The image is virtual.
When parallel rays pass through a converging
lens, the rays converge at the focal point f of
the lens. They form a real image of an object at
infinity.
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Thick and Thin Lenses
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Lens Sign Convention
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Converging Lensesand Special Rays

• A thin lens is defined here as a lens with a
  thickness that is small relative to its focal
  length. We can approximate the lens behavior by
  assuming that the incident rays are bent as they
  pass through the plane of the lens.
• Parallel incident rays are brought to a
  focus beyond the lens at the downstream focal
  point f.
• Incident rays that initially pass through
  the upstream focal point f become parallel
  beyond the lens.
• Incident rays that pass through the center
  of the lens are not deflected.

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Converging Lens Ray Tracing

• Draw the lens.
• Draw the optical axis through the center of the
  lens, with the focal points f placed
  symmetrically on both sides.
• Represent the object with an upright arrow of
  height h at distance s.
• Draw the three special rays from the tip of the
  object arrow(a) A ray from the arrow tip
  parallel to the axis gt right focus(b) A ray
  from the arrow tip through the left focus gt
  parallel(c) A ray from the arrow tip through
  the lens center gt straight.
• Extend the rays until they converge (at the image
  arrow tip).
• Measure the image height h and the image
  distance s.

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Example Finding theimage of a flower
A 4.0 cm diameter flower is 200 cm from the
50-cm-focal-length lens of a camera. How far
should the film be placed behind the lens to
record a well-focused image? What will be
the diameter of the image on the film?
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Magnification

• A positive value of M indicates that the image is
  upright relative to the object. A negative value
  of M indicates that the image is inverted
  relative to the object.
• The absolute value of M gives the size ratio of
  image to object h/h M.

Note that even though M is called the
magnification, its magnitude can be less than
1, indicating that the image is smaller than the
object, (i.e., it is demagnified).
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Virtual Images
The rays diverge from point P on the object
(which is inside f ), are refracted by the lens,
and still diverge after the lens. However, if
the downstream rays are extrapolated backwards,
these extrapolated rays converge to a virtual
image at P. In the case shown, the virtual
image is upright and has a magnification greater
than 1. The rays reaching the eye appear to be
coming from the virtual image.
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Example Magnifying a flower
To better view a flower, a naturalist holds
a 6.0-cm-focal-length magnifying glass 4.0 cm
from the flower. What is the magnification?
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Clicker Question 1
An object is placed between the focal point
of a converging lens and the optical center of
the lens. The image will be (a) Real,
inverted, and enlarged (b) Virtual, upright, and
diminished (c) Virtual, upright, and enlarged
(d) Real, inverted, and diminished.
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Rays and Diverging Lenses

• A lens that is thicker at the edges than at
  the center is called a diverging lens.
• Parallel incident rays, after passing
  through the lens, will diverge from a virtual
  focus point behind the lens, at the upstream
  focal point f.
• Incident rays converging toward the
  downstream focal point f become parallel after
  passing through the lens.
• Incident rays that pass through the center
  of the lens are not deflected.

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Diverging Lens Ray Tracing

• Draw the lens.
• Draw the optical axis through the center of the
  lens, with the focal points f placed
  symmetrically on both sides.
• Represent the object with an upright arrow of
  height h at distance s.
• Draw the three special rays from the tip of the
  object arrow(a) A ray from the arrow tip
  parallel to the axis gt from left focus(b) A
  ray from the arrow tip toward the right focus gt
  parallel(c) A ray from the arrow tip through
  the lens center gt straight.
• Extrapolate these rays backwards until they
  converge.
• Measure the image height h and the image
  distance s.

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Example Demagnifying a flower
A diverging lens with a 50-cm-focal-length
is placed 100 cm from the flower. Where is
the image? What is the magnification?
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ExampleFocal Length of a Thin Lens
The lens shown is made of glass with index
of refraction n 1.50 and has radii of curvature
with magnitudes 10.0 cm and 13.0 cm as shown.
Find the focal length of the lens and its power.
Note that r1 and r2 are both positive in this
example.
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Example Focal lengthof a meniscus lens
What is the focal length of the glass
meniscus lens shown? Is it converging or
diverging?
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Example Designingan eyeglass lens
A plastic (n1.59) eyeglass lens to correct
for near-sightedness is a diverging lens with a
plano-concave design. The patient needs a focal
length of -1.5 m. What is the radius R2 of
the inner surface of the lens?
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End of Lecture 11

• Before the next lecture, read TM, Chapter 32
  again.
• We will have Exam 2 on November 13. There will
  be assigned seating. If you want a left-handed
  aisle seat, a right-handed aisle seat, or a seat
  near the front, of if you require one of the four
  table seats in the back, send me E-mail with your
  request.
• So far 179/196 students have registered their
  clickers. A clicker response that shows up as a
  number may indicate a registration problem.