Wave Optics

1
Wave Optics

• Chapter 24

2
Learning Goals

• Know what conditions are necessary for
  interference to be observed
• Know how light changes phase when it is reflected
  from a surface
• Understand the necessary conditions for
  interference to occur in thin films.

3
Learning Goals

• Explain the polarization of light waves by the
  following methods
• Selective Absorption
• Reflection
• Scattering

4
Conditions for Interference

• The sources must be coherent that is, they must
  maintain a constant phase with respect to each
  other
• The sources must have identical wavelengths
• The superposition principle must apply

5
Change of Phase due to Reflection

• 180o phase change
• Occurs when a ray is reflected from a medium that
  has a higher index of refraction
• No phase change
• Occurs when a ray is reflected from a medium with
  a lower index of refraction

6
Change of Phase due to Reflection
180o phase change
No Phase Change
N1
N1.33
t
N1
7
Interference in Thin Films

• Examine the following
• 180o phase change if n2gtn1
• No phase change if n2lt n1
• ln l/n
• ln is the wavelength of light in the medium
• l is the wavelength of light in a vacuum
• n is the index of refraction of the medium

8
Interference in Thin Films

• Condition for constructive interference
• 2nt (m ½)l
• n is the index of refraction
• t the thickness of the film
• Condition for destructive interference
• 2nt ml
• where m 0, 1, 2, 3,

9
Interference in Thin Films

• Two factors that influence interference
• phase reversals on reflection
• differences in travel distance
• Only holds true when the medium above and below
  the film is the same
• What happens if the medium above and below are
  not the same?

10
Interference in Thin Films

• Newtons Rings
• Result from constructive and destructive
  interference
• Used to test optical lenses
• Supports the wave theory of light

11
Polarization of Light Waves

• Light waves are electromagnetic waves
• E-field wave
• B-field wave
• Light waves are emitted by the vibration atoms or
  molecules of the light source
• the result is an unpolarized light wave

12
Polarization of Light Waves

• Linear polarization of light is a light wave with
  the following properties
• E vibrates in the same direction at all times at
  a particular point
• As the wave propagates in the x-direction, E is
  always in the y-direction

13
Polarization of Light Waves

• Three methods of polarizing light
• Selective Absorption
• Reflection
• Scattering

14
Polarization of Light Waves

• Selective Absorption
• Polaroid Material ( chains of hydrocarbons )
• The direction perpendicular to the molecular
  chains is the Transmission Axes
• Polarizer Analyzer

15
Polarization of Light Waves

• Polarization by Reflection
• If incident Angle is 0o or 90o the reflected
  beam is unpolarized
• If the incident angle is between 0o 90o, the
  light is polarized to some extent
• There exists an angle when the light will be
  completely polarized

16
Polarization of Light Waves

• Polarization by Reflection
• Common when sunlight is reflected by water, snow,
  or glass
• If the surface is horizontal, the reflected light
  has a strong horizontal component.
• The transmission axes is vertical for sunglasses

17
Polarization of Light Waves

• Polarization by Scattering
• Occurs when light is incident on a system of
  particles
• The electrons in the medium can absorb and
  reradiate part of the light.
• The absorption and reradiation of light by the
  medium is what causes sunlight to be polarized

18
Learning Objectives

• Explain how Youngs double slit experiment gave
  credibility to the wave theory of light
• Know how Youngs double slit apparatus created
  areas of constructive and destructive
  interference
• Explain why interference is observed from a
  single slit and diffraction grating.

19
Youngs Double-Slit Experiment

• Double slit experiment of 1801
• Demonstrated constructive and destructive
  interference of light
• Gave credibility to the wave theory of light

20
Youngs Double Slit Experiment

• Interference occurs because of the path
  difference, d, the light waves travel
• Constructive interference occurs when
• d d sin q ml (m 0, 1, 2, )
• Ybright mLl/d (m 0, 1, 2, )
• Destructive interference occurs when
• d d sin q (m ½) l (m 0, 1, 2, )

21
Youngs Double Slit Experiment
22
Diffraction

• Diffraction is the divergence of light from its
  initial line of travel and occurs when waves
• Pass through small openings
• Travel around obstacles
• By sharp edges

23
Single Slit Diffraction

• Diffraction pattern consists of the following
• Central maximum
• Secondary maximum
• Minima
• Each portion of the slit acts as a source of waves

24
Single Slit Diffraction
25
Single Slit Diffraction

• Condition for destructive interference
• sin qdark m( l/a )
• m 1, 2, 3,
• a is the slit width
• Constructive interference
• Occur halfway between the dark fringes
• Central bright fringe is twice as wide as the
  weaker maximum

26
Diffraction Grating

• Consists of many equally spaced parallel slits
• Each slit produces a diffraction

27
Diffraction Grating

• Condition for maximum constructive interference
• d sin qbright ml ( m 0, 1, 2, 3, )
• m is called the order number of the diffraction
  pattern