The momemtum in the x-direction is

          px  =  m * vx



  But deBroglie's formula allows us to switch momentum for wavelength:

                      h
         lambda  =  -----
                      p

  As long as theta is small, and px >> py, then p(tot) ~ px, and

                      h                            h 
         lambda  ~  -----         so    px  ~  ----------
                      px                         lambda


  So the angle theta must be

                         (  py  )            (  h / 2 pi d  )
         theta   ~  atan ( ---- )   =   atan ( ------------ )
                         (  px  )            (  h / lambda  )


                         ( lambda  )
         theta   ~  atan ( ------- )
                         (  2 pi d )


   And for small angles, sin(theta) ~ tan(theta), so


                         ( lambda  )             (      h      )
         theta   ~  asin ( ------- )    =   asin ( ----------- )
                         (  2 pi d )             ( 2 pi d * px )