DO NOW:

1

• DO NOW

2
Do Now (2/18/14)

• Pass in your hw, lab, and Do Now!!!
• A concave mirror with a radius of curvature of
  1.0 m is used to collect light from a distant
  star. The distance between the mirror and the
  image of the star is most nearly

a) 0.25 m b) 0.50 m c) 0.75 m d) 1.0 m e) 2.0 m
3
Objectives

• Describe the causes of interference patterns due
  to diffraction and thin films.
• Use the diffraction equation.
• Describe the effects of polarization of light.
• Determine the wavelength of a light source using
  a diffraction pattern.

4
Brainstorm

• Discuss with your elbow partner (2 min)
• Do you think light is a wave or a particle? Why
  or why not?

5
Intensity

• Is the energy it carries per unit of time.
• Proportional to the square of the amplitude of
  the wave.
• Color of light is related to its ? or f, not
  intensity.
• What characteristic of sound is most similar to
  light intensity?

6
Polarization

• Polarizing filters
• Only possible if light travels as a wave.
• I I0cos2(?) (Maluss Law)

7
Huygens Principle

• In the 17th Century, Christian Huygens proposed a
  theory stating every point on a wave front can
  be considered as a source of tiny wavelets that
  spread out in the forward direction at the speed
  of the wave.

8
Huygens Principle

• Every point of a wave front may be considered the
  source of secondary wavelets that spread out in
  all directions with a speed equal to the speed of
  propagation of the waves.

9
Huygens Principle

• Other scientists immediately understood that
  Huygens principle predicted that all waves
  should then spread into the shadow behind an
  obstacle.
• We call this bending of waves diffraction.
• If light is a wave, it should undergo the process
  of diffraction, and should also be able to
  undergo the process of interference.

10
Light Particle or Wave?

• A light source illuminating a single slit

http//images.google.com/imgres?imgurlhttp//www.
peace-files.com/QF-L-11/07_Double-Slit-03.jpgimgr
efurlhttp//www.peace-files.com/QF-L-11/01_QF-Dou
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11
Light Particle or Wave?

• Particle theory prediction for the pattern
  produced by two slits, side by side

http//images.google.com/imgres?imgurlhttp//www.
peace-files.com/QF-L-11/07_Double-Slit-03.jpgimgr
efurlhttp//www.peace-files.com/QF-L-11/01_QF-Dou
ble-slit.htmlh267w400sz26hlenstart68um
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12
Light Particle or Wave?

• Wave theory prediction for the pattern produced
  by two slits, side by side
• Note to easily observe light-wave interference,
  light from the two sources would have to be
  coherent and monochromatic.

http//images.google.com/imgres?imgurlhttp//www.
peace-files.com/QF-L-11/07_Double-Slit-03.jpgimgr
efurlhttp//www.peace-files.com/QF-L-11/01_QF-Dou
ble-slit.htmlh267w400sz26hlenstart68um
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13
Youngs Double Slit Experiment

• Young saw an interference pattern.
• To explain this alternating pattern of bright and
  dark fringes, he understood that at any point on
  the viewing screen (other than at the center),
  the two rays of light would have to travel
  different distances to arrive at the screen.

x
?
L
14
Youngs Double Slit Experiment

• If this path length difference is an integer
  multiple of the lights wavelength, a bright
  fringe is seen.
• A dark fringe is seen anytime the path length
  difference is ½ of the ?.

?
dsin?
15
Fringes

• Diffraction causes fringes

16
Example Problem 24-1

• 520nm light falls on a pair of narrow slits
  separated by 0.2mm. How far apart are the fringes
  near the center of the pattern on a screen 2.5m
  away?

x 0.064m or 6.4mm
17
Small Angle Approximation

• How could we approximate Youngs formula for
  small angles??

18
Small Angle Approximation

• Note For small angles (x ltlt L), sin? tan?, so
  you can approximate the distance between the
  fringes as

19
Diffraction Gratings

• A special device called a diffraction grating
  consists of many equally-spaced parallel lines
  scratched into a glass plate. The spaces between
  the scratches act as a source of light, and
  interference is observed.
• The interference equation predicts the location
  of maxima in the interference pattern. The maxima
  are much thinner more defined than the pattern
  created by a double slit.
• The only difference about these problems
  (compared to old diffraction problems) will be
  that you wont be told the value of d. Instead,
  youll be told the number of lines per distance,
  which is really 1/d.

20
Review
21
Huygens principle

• Wave theory of light every point on a wave
  front can be considered as a source of tiny
  wavelets that spread out in the forward direction
  at the speed of the wave itself.
• predicts waves bending around openings
• http//www.launc.tased.edu.au/online/sciences/phys
  ics/diffrac.html

22
Diffraction

• Youngs Double slit experiment wave nature of
  light
• dsin? m? - constructive interference
• xm (m ?L)/d

http//www.surendranath.org/applets/optics/slits/d
oubleslit/dblsltapplet.html http//micro.magnet.fs
u.edu/primer/java/interference/doubleslit/
23

• Plane sound waves of wavelength 0.12 m are
  incident on two narrow slits in a box with
  nonreflecting walls, as shown above. At a
  distance of 5.0 m from the center of the slits, a
  first order maximum occurs at point P, which is
  3.0 m from the central maximum. The distance
  between the slits is most nearly
• a) 0.07 m
• b) 0.09 m
• c) 0.16 m
• d) 0.20 m
• e) 0.24 m

24
Single Slit Diffraction

• It turns out that an interference pattern is
  still observed even when theres only one point
  as a source of light.
• According to Huygens principle, each portion of
  the slit acts as a source of waves. Therefore,
  light from one portion of the slit can interfere
  with light from a different portion.

25
Single Slit Diffraction

• The only thing that changes about problems with
  single-slit diffraction is that the interference
  equation now predicts the location of minima
  (where the diffraction pattern has minimum
  intensity), for integral m-values.

26
Different Diffraction Patterns
http//www.tau.ac.il/phchlab/experiments/hydrogen
/diffraction_gratings.htm
27
Diffraction Patterns from Edges

• Diffraction patterns can arise anytime light
  bends when passing around edges of an obstacle.
• Shadows of objects therefore contain diffraction
  patterns, with a bright spot at their centers.
• You should also be aware that light wave
  diffraction isnt observed as much in the
  macroscopic (big) world because diffraction
  effects are more pronounced when the size of the
  opening through which the wave passes is close to
  the size of the wavelength of the wave.

28
Do Now (2/19/14)

• If the distance between two slits is 0.050 mm and
  the distance to a screen is 2.5 m, find the
  spacing between the first and second order bright
  fringes for light of wavelength 600 nm.
• What color is this light?

29
Single Slit Diffraction

• Diffraction of light by a slit of narrow width a

30
Example

• Light of wavelength 580 nm is incident on a slit
  of width 0.3 mm. The observing screen is placed 2
  m from the slit. Find the positions of the first
  dark fringes and the width of the central bright
  fringe.

31
Brewsters Law
32
Polarizing Angle

• The angle of incidence that satisfies Brewsters
  Law.

33
Thin-Film Interference
34
Thin Film Interference

• When light encounters the boundary between two
  substances with different indices of refraction ,
  some of the light will be reflected and some will
  be transmitted.
• Interference happens.
• Constructive interference happens when the 2nd
  wave exits the whole mess in phase with the 1st
  wave.
• ? Depth of film 1/2?

Air (n1.00)
Oil (n1.28)
Water (n1.33)
35
Thin Film Interference

• Destructive interference happens when the 2nd
  wave exits the whole mess out of phase with the
  1st wave.
• ? Depth of film 1/4?

Air (n1.00)
Oil (n1.28)
Water (n1.33)
36
Thin-Film Interference

• When light is reflected upon trying to enter a
  substance with a higher n-value, it is also
  shifted by 180, which is equal to a path
  difference of 1/2?.

Air (n1.00)
Glass (n1.56)
Glass (n1.56)
Air (n1.00)
37
Thin-Film Interference

• Constructive interference will happen when the
  second wave undergoes a total phase change of ?.
• But since during reflection it undergoes a phase
  change of 1/2? when it reflects from the top soap
  layer, it only needs to undergo a phase change of
  1/2? as it travels the thickness of the film
  (twice).

Air (n1.00)
Soap (n1.28)
Air (n1.00)
38
Thin Film Interference

• Constructive
• Destructive

39
Thin Film Interference

• The wavelength of light, ?n, in a medium with
  index of refraction n is
• Where ? is the wavelength of light in free space

40
Example

• Calculate the minimum thickness of a soap-bubble
  film (n1.33) that will result in constructive
  interference in the reflected light if the film
  is illuminated by light with a wavelength in free
  space of 602 nm.

113 nm
41
AP Practice!

• Try to finish the first two problems before the
  end of today.

42
Lab How wide is a human hair?

• A human hair can act just like a double slit. The
  light going around both edges will bend/diffract
  and create an interference pattern.
• This lab will include a writeup

43
Electromagnetic Waves and Optics

• AP PHYSICS
• UNIT 11
• GIANCOLI
• CH.22 - 24

44
Electromagnetic Waves

• We already know that a changing B-field or flux
  will produce an electric field (i.e. causes the
  movement of charges or current)
• Conversely, James Maxwell came up with the idea
  that a changing electric field can produce a
  magnetic field.

45
Electromagnetic Waves

• Accelerating charge gives rise to EM waves that
  can even travel through a vacuum.
• The oscillating electric and magnetic fields are
  perpendicular to one another.
• EM waves move through a vacuum at c
  3.00x108 m/s.

46
Electromagnetic Waves

• The wave-speed equation still applies

47
Speed of Light (c)

• Ole Roemer first determined that the speed of
  light was finite.
• He found that the period of Io, one of Jupiters
  moons, varied slightly depending on the relative
  motion of Earth and Jupiter.
• If the Earth was moving away from Jupiter during
  Ios orbit the light would have to travel a
  longer distance, increasing I0s apparent orbital
  period.

48
Electromagnetic Spectrum
49
Inverse Square Relationship
50
Ch.22 Homework

• Read sections 22.1 22.2 (no math in either),
  22.3-22.4 and 22.7
• Questions 1, 3, 5, 10 13
• Problems 5-6, 9 16
• Due Tomorrow

51
Ch.22 Homework Answers

• 5. 1.88E10 Hz
• 6. 1.008E-10 m
• 9. 8.33min
• 16. radio hears 0.14s soon

52
Physics of Sight

• We see an object in one of two ways
• The object is a source of light (sun, fire, light
  bulb filament)
• The object reflects light
• Reflected Light rays scatter from each point on
  an object.
• Our brains construct the image of an object
  assuming that the light entering our eyes travels
  in straight lines.

53
Law of Reflection

• The angle of reflection is equal to the angle of
  incidence.

?1
?2
?1
?2
54
Plane Mirrors

• The image formed by a plane mirror is a virtual
  image (cannot be projected onto a screen)

55
Spherical Mirrors

• Concave mirrors reflect incoming parallel light
  rays so that they pass through a common focal
  point
• Convex mirrors reflect incoming parallel light
  rays so that they appear like they are coming
  from a focal point behind the mirror.

56
Spherical Mirrors

• C Center of curvature
• F focal point
• r radius of curvature
• f focal length

C
F
C
F
f
57
Spherical Aberration

• Technically speaking spherical mirrors do not
  focus the rays perfectly. And the more spherical
  a mirror is, the more the image will appear
  blurred. This defect is called spherical
  aberration. For very sensitive applications
  parabolic mirrors are used.

http//wisp.physics.wisc.edu/astro104/lecture7/F06
_13.jpg
58
Concentrating Solar Power (CSP) Plants

• The suns rays are focused on pipe filled a fluid
  to collect the energy in order to generate
  electricity.

http//images.google.com/imgres?imgurlhttp//www.
flabeg.com/images/g_03_solar_mirrors.jpgimgrefurl
http//www.flabeg.com/en/03_solar_mirrors.htmlh
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http//en.wikipedia.org/wiki/Solar_thermal_energy
High-Temperature_Collectors_Concentrated_solar_po
wer_.28CSP.29_plants
59
Drawing Ray Diagram Rules

• Rule 1 Draw a ray going out from the object
  parallel to the principal axis that reflects back
  through the focal point.

60
Drawing Ray Diagram Rules

• Rule 2 Draw a ray that goes through the focal
  point (or in a direction like it came from the
  focal point) then reflects back parallel to the
  axis.

61
Drawing Ray Diagram Rules

• Rule 3 Draw a ray from the object through the
  center of curvature. This ray will strike the
  mirror at a right angle and will reflect back on
  itself.

62
r gtobject distance gt f
focal point is
Image is Real, larger inverted
63
object distance lt f
Image is Virtual, larger upright
64
Ray Diagram for Convex Mirror
Image is always Virtual, smaller upright
focal point is (-)
Uses rear view mirror, convenience store mirror
65
The Mirror Equation

• h0 is always ()
• hi is () if upright, (-) if inverted with
  respect to the object
• ()si ? image in front of mirror
• (-) si ? image behind mirror
• f () for concave mirrors, (-) for convex mirrors

66
Example Problem 23-4

• A 10cm-tall object is placed 12cm in front of a
  convex mirror that has a radius of curvature of
  35cm. Completely describe the reflected image.
  (What is its location? Its height? Is it real or
  virtual? Upright or inverted?)

si -7.1cm, hi 5.92cm, virtual and upright
67
Example Problems 23-4 and 23-5

• A concave mirror with a radius of curvature of
  14cm is used to focus the Suns rays. Where are
  the rays focused, relative to the surface of the
  mirror?
• You are standing 3.0m from a convex security
  mirror in a store. You estimate the height of
  your image to be half of your actual height.
  Estimate the focal point of the mirror.

7cm from the surface of the mirror at the focal
point
f -3m
68
Refraction

• All lenses redirect light rays by the process of
  refraction

n1
n2
?2
?1
69
Lenses

• Lenses can be grouped into two main categories
  converging and diverging lenses.

70
Ray Diagrams for Lenses
71
Example Problem

• Use a ray diagram to show the image height and
  position for the given object.

F
F
72
Thin Lens Calculations

• The mirror equation still applies, but now its
  called the thin lens equation. (The magnification
  equation is still the same, too.)
• Sign conventions for using the equations are
  somewhat different now
• s0 is () if it is on the same side of the lens
  as the incoming light which is most of the time.
  
• If si is () then the image is on the opposite
  side of the incoming light, (-) if on the same
  side.
• f is () for converging lenses, (-) for diverging
  lenses.

73
Multiple Lenses

• If two thin lenses in a row are used to form an
  image, first find the image of the first lens
  alone. Then the light approaches a 2nd lens as if
  it had come from the image. This means that the
  image formed by lens 1 becomes the object for
  lens 2.

F
74
Multiple Lenses

• The magnification for multiple lenses is just the
  product of the individual magnifications of lens
  1 2.
• (Example) Two converging lenses, each of focal
  length 20cm, are place 50cm apart from one
  another, and an object is place 10cm to the left
  of the first lens. Where is the final image
  formed, and what is the magnification of the
  entire system?