To get a better resolution the idea is to reduce d. Since the constant 2440 and Lambda can't be changed, the only way to reduce d, is to reduce N.  Likewise the only way to reduce N is to shorten f, the focal length, as the lens or mirror only has one diameter.
For example: An 8" telescope with a focal length of 3,048 mm will have a Focal Ratio N, of F:15.  The diameter of the Airy disk will then be: 2440 * 550e-9 * 15 = 0.02mm.
This yields a Diffraction Limited Resolution of R = 2 / .02 = 100 lines per millimeter.  Shortening the focal length to 812.8 mm will give the same 8" telescope a Focal Ratio N, of F:4.  The new diameter of the Airy disk will be 2440 * 550e-9 * 4 = 0.0053mm.  This results in a Diffraction Limited Resolution of R = 2 / 0.0053 = 377 lines per millimeter.
A lens or mirror that contains aberrations that exceed a 1/4 wavefont error will produce Airy disks larger than the Airy disks described above.