title: Wavefronts and Rays: As Characteristics and Asymptotics
author: Michael A Slawinski
description: This book ... leads the reader from the simple to the complex, but which also includes a variety of physical sciences applications. It is a bridge between mathematicians, mathematical physicists, and applied scientists in all fields who study wave propagation and employ ray theoretic methods. -- The Leading Edge "The Leading Edge"
zlib_text: Ch. 35   p. 1 
   
  CHAPTER 35 – The Wave Nature of Light; Interference 
   
  1. 
  We draw the wavelets and see that the  
   
  incident wave fronts are parallel, with  
   
  the angle of incidence θ1 being the angle  
   
  between the wave fronts and the surface.   
   
  The reflecting wave fronts are parallel,  
   
  with the angle of reflection θ2 being the  
   
  angle between the wave fronts and the 
  surface.   
   
  Both sets of wave fronts are in the same  
   
  medium, so they travel at the same speed.   
   
  The perpendicular distance between  
   
  wave fronts is BC = AD = c ?t.   
   
  From the triangles, we see that  
   
   
  AB = BC/sin θ1 = AD/sin θ2 . 
   
  Thus we have 
   
   
  sin θ1 = sin θ2 ,   or   θ1 = θ2 . 
   
  2. 
  For constructive interference, the path difference is a multiple of the wavelength: 
   
   
  d sin θ = mλ,   m = 0, 1, 2, 3, … . 
   
  For the fifth order, we have 
   
   
  (1.6 × 10–5 m) sin 9.8° = (5)λ, which gives λ = 5.4 × 10–7 m =      540 nm. 
   
  3. 
  For constructive interference, the path difference is a mult