Chapter 37:  Interference of Light Waves 

 

Learning Goals

  1. Understand Young's double slit experiment.
  2. Understand phase changes for reflection.
  3. Understand interference in thin films.

 

Interference

Interference occurs whenever light waves from two or more sources overlap at a given point. Interference patterns which remain stationary in time occur under the following circumstances:
  1. all sources are coherent
  2. each source has identical wavelength (beats for optical frequencies are too rapid to observe without very sophisticated equipment)

 

Young’s Double Slit Experiment

Sir Thomas Young achieved both conditions above by illuminating a double-slit aperture by filtered light which first passed through a tiny hole. He observed bright and dark interference fringes on a screen a distance L away with positions given by:

 

Bright fringes:      d sin(q) = ml, ybright = mlL/d
Dark fringes: d sin(q) = (m + ½)l,      ydark = (m + ½)lL/d

where l is the wavelength, d is the slit spacing, and m = 1, 2, ... is the order number.

The importance of Young’s experiment was that it unambiguously demonstrated the wave nature of light.

 

Interference in Thin Films

Thin films (such as oil films on the surface of water) can exhibit interference effects. Such films have many useful applications, such as anti-reflection coating on camera lenses.

The following concepts are central to understanding interference in thin films:

Phase changes on reflection: a wave reflecting from a region of higher index of refraction is phase-shifted by 180°. There is no phase change for a wave reflecting from a region with lower index of refraction.

Optical thickness: since the wavelength of light decreases when it enters a region with greater index of refraction, the optical thickness nt is greater than the physical thickness t of a film.