How can the Airy's equation $y'' - xy = 0$ be used to model diffraction of light? Differential Equations with Boundary-Value Problems by Dennis G. Zill, Michael R. Cullen states that the equation is used to model diffraction of light. It doesn't explain how, it just goes on to solve it using a series solution. 
Has anyone any idea how it is used or has any references? Or if anyone knows any other applications of this equation then that would be interesting also :) 

Here is a reference to a 1977 article by H. M. Nussenzveig in Scientific American about the Theory of the Rainbow.  The captions of the figures in the article are informative.
The differential equation also appears in Professor Nussenzveig's 1992 book Diffraction Effects in Semiclassical Scattering.
