It can be shown that the average intensity of the single-slit pattern is:

Iav

=

Imax

[

sin [pa sin(q) / l] pa sin(q) / l

]

2

For small angles

sin(q)

=

y L

so:

Iav

=

Imax

[

sin [pa y / (lL) ] pa y / (lL)

]

2

where y is the distance along the center of the screen measured from the center.