Light Inteference ------------------------------------ Joseph F. Alward, PhD       Department of  Physics       University of the Pacific

Applets used in this eLecture: Young's Double Slit 1 Young's Double Slit 2

  Light is a Wave-Like Disturbance                                               

  Constructive Interference                                                        

Waves from two sources start out in phase. Constructive interference occurs if:       d2 - d1 =  n l      n = 0, 1, 2, 3, ..... ---------------------------------- Difference must be an integer number of wavelengths

  Destructive Interference                                                                                         

Waves from two sources start out in phase. Destructive interference occurs if: d2 - d1 =  (2n + 1) (l/2)       n = 0, 1, 2, 3, .... ---------------------------------- Difference must be an odd half-integer number of wavelengths.

 Inteference of Waves from Two Sources                                             

In some places the water wavefronts are in phase (bright spots). In other places the fronts overlap with peak and valley and interfere destructively (darker spots).

  Interference of Two Sources                                                       

Destructive interference occurs whenever the airplane's position is such that L2 - L1 = l/2 -------------------------------------------- Destructive interference also occurs for L2 - L1 = 3 (l/2) .....and so on.

 Young's Double Slit Experiment                                       

 Young's Double Slit          

Thomas Young  (1801)

  Young's Double Slit Applets

Young's Double Slit 1  Green laser cannon    Young's Double Slit 2 Vary color, distance, intensity, slit separation, see graph of intensity

 Constructive Inteference                                                                                        

For a bright band at P:     l = d sin q     or   2l = d sin q      or   3l = d sin q          etc For a given  l, bright bands occur at sin q  =      0                        =       l/d                      =  2 l/d                       =  3 l/d  d sin q  = m l,       m = 0, 1, 2, ....

  Double Slit Geometry                                    

 More Double Slit Geometry                               

tan q  = y / L        (1)       y = L tan q     (2) --------------------------- If the values of q at which maxima occur are known from d sin q  = m l then the values of y at which bright spots appear may be calculated.

 Reflection in Thin Films                      

Rays 1 and 2 interfere -------------------------------- Wavelength inside film is smaller:   l' = l / n n = index of refraction       of film ------------------------------- Ray 1 suffers a phase change of 180 degrees

   Phase Change on Reflection                              

   Non-Reflective Coatings                                            

What must be the thickness t of silicon oxide for zero reflection of l = 550 nm? ----------------------------------------------------- Since the phase changes cancel, we need a one-half wavelength shift as Ray 2 travels the extra distance 2t:     ----------------------------------------------------- Wavelength in SiO:          l' = 550 nm /1.45              = 379.3 nm -----------------------------------------------------         2t  = (379.3 nm) / 2           t  = 94.8 nm

   Light Interference in Thin Films Example                            

Ray 2 experiences a half-wavelength phase change.  For dark fringe, need 2t =  l.

  Light Inteference in Soap Film                                               

Soap film on rectangular frame is similar to glass plates with air film between them.

  Newtons' Rings                                                                                   

Plano-convex lens on flat black surface

   Newtons' Rings Explained                                                              

  Glass Wedge                                                                                                         

Air is above and below glass wedge   Phase change at top of wedge No phase change at bottom -------------------------------------------------- Dark condition: 2t  =    1 (l /n)              2 (l /n)                  3 (l /n) Bright condition: 2t  =   1 (l /n) /2           3 (l /n) /2           5 (l /n) /2

   Inteference Projects                                                                                          

Thin film of air between slides produces  interference pattern.

   Thin Film Interference in Peacocks                     

Iridescence of peacock feathers is caused by light reflected from complex layered surface