Wave Nature of Light: Interference and Diffraction

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PH103
Wave Nature of Light Interference and Diffraction
Dr. James van Howe Lecture 9
March 31, 2008
Water wave diffraction Sitges, Barcelona
Photo Barcelona Field Studies Center
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In the television program The Office, Andy
Bernard constantly drops the name of what
east-coast university where he participated in an
a capella group?

• Dartmouth
• Cornell
• Rutgers
• Yale

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True or False
In a microscope, increasing the focal length of
the objective lens increases the angular
magnification
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Diffraction
If light hits an opening, the beam will be
bent/spread.
Spreading will be the most for
A.
B.
C.
D. None, they spread the same in each
case
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Telescope Extended Object
Rays from infinity
Objective lens
Eye Piece
h
o
I
I
h
Light gathering power
Virtual rays to infinity
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Telescope Point Object
Objective lens
Eye Piece
o, point object
I, image just a point
Light gathering power
Focus of lens not doing much rays of light so
far away they come in at no angle
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MCAT Telescope Questions
17. Which telescope would require the least
amount of time to observe a star 800 kpc away?
(note 1 kpc 3 x 1016 m)
Telescope A The larger diameter, the larger the
light gathering power, the more efficient the
lens, the less time needed
Since looking at point object far away
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18. If an eye has a diameter of 0.5 cm, what is
the light gathering power of Telescope A compared
to the eye?
Unclear question if you know about telescopes.
Are we looking at a point object or an extended
object? If we blindly follow the reading which is
not the whole truth, we are only given Which is
only true of point objects. If this is a point
object,
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19. Why are large telescopes most often
reflecting telescopes?

• Lenses always magnify more than mirrors
• Large lenses cannot hold their shape
• Large lenses produce greater aberration

-Weight of glass deforms under force of gravity,
so changes lens shape. In a reflecting telescope
you can ideally paint on a reflecting surface
(make it thin)
-One reason large lenses produce greater
aberration is the glass causes colors to travel
at different speeds. Different colors will focus
in different places.
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Dispersion
The property of wave where different frequencies
(colors, if we talk about light) travel at
different speeds through a dense medium. Index of
refraction depends on color of light.
Why does this happen?
nucleus
Electron, -q
m
Electron responds differently to different
frequencies. For example at the resonance
frequency we have the most delay (greatest index
of refraction).
In the prism, blue light bends more than red, so
what color travels faster?
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20. One of the advantages of using large
telescopes as compared to small telescopes is
that

• large telescopes magnify distant star images more
• large telescopes shorten the observing time
  necessary to complete an observation
• large telescopes track a star with greater
  accuracy.
• large telescopes have a better dynamic range

A. is only true if the focal length is lengthened
at the same time, but it is unclear that this is
the case. The question just considers larger
diameter. So B is the only one that makes sense.
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21. Which Telescope would enlarge an image of the
Andromeda galaxy the most?
Dont over-think this one, the answer is
Telescope E. The fact that it is a galaxy just
lets you know that the telescope will actually
be magnifying. Distant point objects dont
magnify much at all.
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22. Which of the following statements describes
why the use of mirrors decreases the degree of
chromatic aberration?

• Lenses refract light at an angle that depends on
  its wavelength, whereas mirror reflect light of
  all wavelengths at the same angle.
• A mirror absorbs much less light in reflecting
  than a lens absorbs in refracting
• Since mirrors are easier to grind accurately than
  lenses, mirrors have fewer flaws than lenses.
• The changes in temperature during the course of
  an evening affect mirrors less than lenses

Basically if you use a lens, you will have a
prism effect, dispersion. In a mirror the
reflected light does not travel into a dense
optical medium like glass but reflects off of the
surface. So with a mirror you will not have
dispersion and therefore no chromatic aberration.
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23. The passage states that for observation of
faint extended objects, magnification is not the
primary factor. Which of the following best
describes what would happen to an image of a
faint galaxy as the magnification is increased

• The image would get larger and dimmer, eventually
  fading completely because the small amount of
  light coming from the galaxy would be spread over
  a larger image area.
• The image would remain the same size and become
  dimmer, because there is an intrinsic upper limit
  on how much any telescope can enlarge an image.
• The image would get larger indefinitely,
  remaining at the same overall brightness, because
  there is no intrinsic limit on how much any
  telescope can enlarge an image.
• The image would get larger and dimmer, eventually
  fading because of dispersion effects.

As you magnify an extended object, it does get
magnified and fainter since light is spread out
over a larger area. It doesnt really fade
completely. You could use film and wait a long
time and it would show up.
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Recall EM plane wave looks like
, wavelength (spatial period)
distance
We are looking at the wave in a snapshot of time,
I can write it just as a function of space as
shown below.
D
Electric Field, E
distance, z
Electric Field
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Time dependence
, wavelength (spatial period)
x
distance
If we sit on one crest (like at the smiley face)
we see that the amplitude also goes up and down
like a sine wave as a function of time.
D
Electric Field, E
time, t
Electric Field
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Constructive Interference
Source 1
Source 1
Two beams of light at the same frequency and same
amplitude, in phase (0, 2p, 4p radians out of
phase even multiples of p), at the same amplitude
position, z
Final Electric Field
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Destructive Interference
Source 1
Source 1
Two beams of light at the same frequency and same
amplitude, but out of phase (p, 3p, 5p radians
out of phase odd multiples of p),
position, z
Electric Field, E
Final Electric Field
Same thing happens in noise canceling headphones
and auto mufflers
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Huygens-Fresnel Principle
Every point on a wavefront serves as a secondary
source of point sources

Plane Wave, Arial View
Infinite amount of point sources plane wave
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Waves will diffract around a barrier
Bending
Many point sources, but not infinite
Plane Wave
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Diffraction by a Single Slit
Case 1
Infinite point sources fit inside aperture
Shadow
plane wave out
Bright
Like light going through a window
Shadow
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Diffraction by a Single Slit
Many point sources, but not infinite
spreading
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Diffraction by a Single Slit
Slit so small only one point source fits
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Double Slit Diffraction
like two point sources
could be two speakers, small slits for light, two
stones on pond
Lines of constructive interference
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Poissons Spot
If obstruction size is on the order of
wavelength diffraction
Bright spot behind obstacle
Demo Video ripple tank, acoustic Poisson
Demo optics card
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Interference The property of waves to add up
(superpose) constructively or destructively
In order to have good interference, the waves
have to be coherent
Coherent source when any two waves emitted from
that source have a fixed relationship in
time/space
Wave 1
Good coherence Good interference
Wave 2
Example laser
Wave 1
Wave 2
Bad coherence Bad interference
Example sunlight