Interference

1
Interference

• Interference of waves requires
• The sources must be coherent
• The waves must have identical wavelengths
• Coherence means waves must maintain a constant
  phase with respect to each other
• Two sources are needed to create interference

2
Coherence

• Ordinary light is incoherent
• Two separate sources are not in phase over a long
  period
• Ordinary light undergoes random changes on the
  order of once per 10 ns.
• Can create coherence by using a monochromatic
  source shining through two narrow slits a short
  distance apart

3
Youngs Double Slit Experiment

• Define the path difference as

• Constructive interference occurs when

• Destructive interference occurs when

4
Small angle approximation

• When distance to screen is large compared with
  distance between fringes, angle is small
• Can approximate sin q as

• where y is the distance between fringes and L is
  the distance to the screen

5

• A laser beam has a wavelength of 632.8 nm. It is
  incident on two slits 0.200 mm apart. How far
  apart are the bright interference fringes on a
  screen 5.00 m away from the double slit?

6
Diffraction

• Whenever a wave encounters an obstruction, the
  wave bends around it
• Explained by Huygens Principle
• Each point acts as source of a spherical wave

7

• Waves generated by edges of slit superimpose on
  each other
• Acts in a manner similar to two slits, and so
  generates an interference pattern

8

• Destructive interference occurs when

9
Polarization

• Transverse waves can be polarized if the
  direction of oscillation is in the same direction
  all of the time.
• Light can be polarized by
• Selective absorption
• Reflection
• Scattering

10
Intensity of polarized light

• Let unpolarized light have an intensity of I
• Polarized light has an intensity of I0 I/2
• When passed through a second polarizer whose axis
  makes an angle of q with respect to the first
  polarizer, the resulting intensity is