|Understanding Fraunhofer Diffraction|
Learning Goal: To understand the derivations of, and be able to use, the equations for Fraunhofer diffraction.
Diffraction is a general term for interference effects related to edges or apertures. Diffraction is more familiar in waves with longer wavlengths than those of light. For example, diffraction is what causes sound to bend around corners or spread as it passes through a doorway. Water waves spread as they pass between rocks near a rugged coast because of diffraction. Two different regimes for diffraction are usually identified: Fresnel and Fraunhofer.
Fresnel diffraction is the regime in which the diffracted waves are observed close (as compared to the size of the object causing the diffraction) to the place where they are diffracted. Fresnel diffraction is usually very complicated to work with. The other regime, Fraunhofer diffraction, is much easier to deal with. Fraunhofer diffraction applies to situations in which the diffracted waves are observed far from the point of diffraction. This allows a number of simplifying approximations to be used, reducing diffraction to a very manageable problem.
An important case of Fraunhofer diffraction is the pattern formed by light shining through a thin slit onto a distant screen (see the figure).
Notice that if the light from the top of the slit and the light from the bottom of the slit arrive at a point on the distant screen with a phase difference of , then the electric field vectors of the light from each part of the slit will cancel completely, resulting in a dark fringe. To understand this phenomenon, picture a phasor diagram for this scenerio (as show in the figure).
A phasor diagram consists of vectors (phasors) with magnitude proportional to the magnitude of the electric field of light from a certain point in the slit. The angle of each vector is equal to the phase of the light from that point. These vectors are added together, and the resultant vector gives the net electric field due to light from all points in the slit. In the situation described above, since the magnitude of the electric field vectors is the same for light from any part of the slit and the angle of the phasors changes continuously from to , the phasors will make a complete circle, starting and ending at the origin. The distance from the origin to the endpoint of the phasor path (also the origin) is zero, and so the magnitude of the electric field at point is zero.