As a numerical example, let’s look at the case of the output from a Newport R-31005 HeNe laser focused to a spot using a KPX043 Plano-Convex Lens. This Hene laser has a beam diameter of 0.63 mm and a divergence of 1.3 mrad. Note that these are beam diameter and full divergence, so in the notation of our figure, y_{1} = 0.315 mm and θ_{1} = 0.65 mrad. The KPX043 lens has a focal length of 25.4 mm. Thus, at the focused spot, we have a radius θ_{1}f = 16.5 µm. So, the diameter of the spot will be 33 µm.

This is a fundamental limitation on the minimum size of the focused spot in this application. We have already assumed a perfect, aberration-free lens. No improvement of the lens can yield any improvement in the spot size. The only way to make the spot size smaller is to use a lens of shorter focal length or expand the beam. If this is not possible because of a limitation in the geometry of the optical system, then this spot size is the smallest that could be achieved. In addition, diffraction may limit the spot to an even larger size (see Gaussian Beam Optics), but we are ignoring wave optics and only considering ray optics here.

Another common application is the collimation of light from a very small source, as shown in Figure 6. The problem is often stated in terms of collimating the output from a “point source.” Unfortunately, nothing is ever a true point source and the size of the source must be included in any calculation. In figure 6, the point source has a radius of y_{1} and has a maximum ray of angle θ_{1}. If we collimate the output from this source using a lens with focal length f, then the result will be a beam with a radius y_{2} = θ_{1}f and divergence angle θ_{2} = y_{1}/f. Note that, no matter what lens is used, the beam radius and beam divergence have a reciprocal relation. For example, to improve the collimation by a factor of two, you need to increase the beam diameter by a factor of two.