Path difference can explain interference patterns seen by Thomas Young.  Each wave must travel a certain length, along a specific path, from the slit to the distant screen.

 


 

The length from any one point on the screen to each slit is slightly different, as shown in d 1 and d 2 because the slits are located apart from each other.  This means that light leaving both slits must travel slightly different lengths, d 1 and d 2 , to arrive at the same spot on a distant screen.  The difference in the path lengths is called the path difference.


Path difference, Δd = | d 1  -  d 2 |

 

If the path difference to a common point on the screen is an integral number of wavelengths, then the waves arrive at the common point in phase and constructively interferes producing a bright fringe.  However, if the path difference is a half-number of waves, then the waves arrive completely out of phase and destructively interfere leaving a dark fringe.

 

Path difference explains the interference patterns created by two-slit diffraction.  When the light reaches a screen, bright and dark bands are observed.  These bands are called interference fringes.   Bright fringes  (antinodal lines)  are regions of constructive interference and  dark fringes  (nodal lines)  are regions of destructive interference.  The following image illustrates the fringes and the path differences for the interference pattern created when light is diffracted in a two-slit experiment.  Notice that the bright and dark fringes are symmetrical around the central antinode.



Bright Fringes:  regions of constructive interference along antinodal lines

 

Dark Fringes:  regions of destructive interference along nodal lines


Read
Read "The Interference Pattern" on pages 686-687 of the textbook.  Review figures 13.72 to 13.74 which illustrate the path difference explanation.  These figures will help with the self-check questions below.


Self-Check

Answer the following self-check (SC) questions then click the "Check your work" bar to assess your response.

  

SC 1.

Why is there always a bright fringe at the centre of the screen? (This fringe is called the central antinode.)

 

SC 2.  

Explain why this central antinode is always the brightest fringe.

 

   Self-Check Answer

Contact your teacher if your answers vary significantly from the answers provided here.

 

SC 1.
The central antinode is the result of constructive interference. The path length from each hole in the grating to the central antinode is identical so the path difference is zero (as shown in the diagram). Both waves arrive in phase and interfere constructively to produce the bright fringe.

 


 

SC 2.

All of the waves arriving at the central antinode are completely in phase, causing complete constructive interference. The other bright fringes will have some destructive interference due to multiple slits or the light is naturally dimmer because it is not the first order maximum, which is the brightest.