Rami Arieli: "The Laser Adventure" Pinhole Lab., Page 3
Theory of Pinhole Diffraction:

The angle (q ) at which the first diffraction minimum occurs when light diffracts through a circular pinhole is given by:

             (1)


Figure Pin1: Theory of diffraction through Pinhole.

If L>>D, i.e. if we observe the bright spot which is a few centimeters in diameter on a wall which is a few meters away.
Then it is to use the small angle approximation:

sinq »q = ½ (D/L)       (2)

From equations (1) and (2) we get:

    Þ       (3)