INTERFERENCE

I. If we have waves coming from two sources that are in phase and have the same frequency, then the waves can be added at some observation point using the principle of superposition. We say that the waves interfere with each other and we can look at two extremes:

  A. Constructive interference occurs when the waves add to produce a resultant wave with twice the amplitude







  B. Destructive interference occurs when the waves add to produce a resultant wave with zero amplitude







  C. What are coherent sources?

  D. The condition for constructive interference for two coherent sources is that the paths the waves travel to the point of
  observation differ by some integral number of wavelengths

   path difference = (integer) x (wavelength)



  E. The condition for destructive interference for two coherent sources is that the paths the waves travel to the point of
  observation differ by some odd multiple of one-half a wavelength

   path difference = (odd integer) x (wavelength)/2







II. Thomas Young's experiment is an example of the interference of light and demonstrated that light has wave-like properties.

  A. Describe the set-up for his experiment and give the equations that result for constructive and destructive interference.














III. When we have neither "purely" destructive nor "purely" constructive interference, and the light waves arrive at the point of observation with some general phase difference, we can use the method of phasors to find the resultant wave.











IV. Phase differences can also occur as a result of reflection. If light reflects from the surface of a material that has a higher index of refraction than the medium in which the light originates, then the reflected light is 180 degrees out of phase with the incident light.

V. Phase changes on reflection have to be taken into account when we look at light reflected from thin films, such as coatings placed on camera lenses or thin oil films floating on water.

  A. For thin film interference we have to remember

   1. The wavelength of the light in the film is different than it is in air

   2. Phase changes can take place for the reflected light when it reflects from a material of higher refractive index.

   3. Phase differences can occur if two reflected light waves come from two different points in the film and travel different path    lengths to the point of observation




















EXAMPLES

Text Chapter 36: Problems 15, 42