What is Fraunhofer Diffraction


Fraunhofer diffraction at the slit



Phase difference:


Every point x of the opening is the starting point of an elementary wave (Huygens principle). The superposition of all partial beams diffracted at the angle F corresponds to a summation of the field strengths from x = 0 to x = b (with a fixed F) in the direction kF. outgoing partial waves and results in the field strength at the wave front taking into account the phase relationships




The angle element DF / p corresponds to the proportion of that emanating from the gap b Elementary waveswhich is scattered in the direction of F, F + DF. The ratio (Dx / b) corresponds to a portion of the beam of width Dx passing through the gap b.


Using the expression for the position-dependent phase differencewe get the field strength



This gives the amplitude of the field strength as a function of the angle F:



The intensity is proportional to the square of the amount of the field strength:

By means of relationships


we receive








Calculation of the intensity minima





The condition for intensity minima results from this



(Note: For diffraction at the grating, this is the condition for intensity maxima!)



Calculation of the intensity maxima


It's the problem


to solve for the occurrence of relative maxima.

The intensity equation can be in the simplified form



write down. By differentiating for a and setting to zero it follows




So the transcendent equation must be



be solved.


This equation has the solutions




Where the coefficients km Solutions to the equation


are with