How does intensity vary across screen in single slit diffraction?

[j-lee00]

Why( and how) does the intensity of the wave vary along a screen perpendicular to the optical axis?

 

[jtbell]

The light arriving at the screen is the superposition (sum) of waves from the various parts of the slit. In general, these waves each travel slightly different distances to reach a particular point on the screen, and so they interfere with each other. The amount of interference varies from one point to another on the screen.

Examples:

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/fraungeo.html#c1

One way to derive the formula that gives the intensity at various points on the screen:

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinint.html#c1