Superposition

3.2   Overlapping waves:

1. What will happen when waves overlap?    

2. 1d superposition of waves generated by two coherent sources     

3. Superposition principle

   • Addition of the individual displacements at any point

   • Superposition of waves from two sources

   • Vector model for the resultant amplitude

   • Intensity =  | Ares |^2

Phase difference between the oscillating sources       Usually the sources oscillate in phase        

Path difference at a location P        

Phase difference between the waves at a location P Conditions for maxima and minima

phase difference = 2*pi*(path difference / wavelength) 

Conditions for maxima and minima

Constructive interference          Ares = 2A     If path difference is integer number wavelengths

Destructive  interference         Ares = 0        If path difference is half integer number wavelengths

Just interference         Ares = 2A* | cos(phi/2) |  

4. What a coherent source of waves means?             

3.3  Double slit experiment

1. Monochromatic wave    Slit separation       Interference pattern on the screen

2. Maxima order     Number of  maxima

3. Formula  for angular distribution of  maxima  and minima

4. Distance to the screen and  fringes separation

5. Hyperbolas

6. How Young made coherent wave

3.4  Many slits  interference

1. Diffraction grating and distance to the screen

2.  Slits per unit length and diffraction grating constant

3. Formula for angular distribution of maxima         

4. Intensity distribution  for N slits    

5. Intensity for N slits by phasors

3.5  Diffraction

1. Single slit diffraction pattern         Equation for the minima          **Intensity formula          

2. Divergence of a beam           

3. Diffraction by finite barrier