P to the different points L,M,N, etc., can be treated as parallel, making an angle with the normal MC. The basic idea is to divide the slit into much smaller parts, and add their contributions at P with the proper phase differences. We are treating different parts of the wavefront at the slit as secondary sources. Because the incoming wavefront is parallel to the plane of the slit, these sources are in phase.
The path difference NP – LP between the two edges of the slit can be calculated exactly as for Young’s experiment. From Fig. . , NP – LP = NQ = a sin a ( .
) Similarly, if two points M and M in the slit plane are separated by y , the path difference M P – M P y . We now have to sum up equal, coherent contributions from a large number of sources, each with a different phase. This calculation was made by Fresnel using integral calculus, so we omit it here. The main features of the diffraction pattern can be understood by simple arguments.
At the central point C on the screen, the angle is zero. All path differences are zero and hence all the parts of the slit contribute in phase. This gives maximum intensity at C. Experimental observation shown in