Two Slits Experiment: Calculating Intensity with Transverse Momentum

[maria clara]

Problem: A monochromatic source with wavelength lambda and amplitude E0 is
located behind a wall with two very narrow slits. The separation between the
slits is d. We would like to calculate the intensity I(k(transverse)) on a screen located
z = L where L >> d.

Solution: We can consider the two slits as two monochromatic sources.
The outgoing field from each slit can be approximated (for simplicity) by a
wave from a point source with amplitude E0 and wavelength lambda. At each point
of the screen the intensity depends on the total field, i.e. the sum of the two
fields..
after calculating the sum we get an expression which is a function of the transverse momentum..
Could anyone explain what is the exact connection (in the physical manner of course) between the transverse momentum and the intensity?

 

[BigJDubs]

The connection between transverse momentum and intensity is that the transverse momentum determines the angle of the wavefronts arriving at the screen, which in turn affects the interference pattern of the two waves. When the angle of the wavefronts is such that the waves are in phase (i.e., when they are at a maximum of their oscillation), constructive interference occurs, resulting in a bright spot on the screen. Conversely, when the wavefronts are out of phase (i.e., when they are at a minimum of their oscillation), destructive interference occurs, resulting in a dark spot on the screen. The transverse momentum thus determines the amplitude of the interference pattern, and hence the intensity.