I'm not completely au fait with the maths, but basically, the smaller a lens or mirror is, the less sharply it will focus a beam. Using smaller apertures on a camera lens will increase apparent sharpness of the image until you get to the size where the rays start diffracting, at which point detail starts getting more blurred.
Going the other way, the bigger the searchlight lens/mirror combination, the more parallel you can make the light rays in the beam. It also affects radio transmissions and sound recording using parabolic reflectors, where the bigger the dish, the smaller the beam angle.
If you want the gory details, then search for diffraction limit on Google.