Infinity in Optics
Infinity comes up often in optics when talking about the curvature of surfaces. Most commonly when referring to mirror surfaces or lens curvatures. These surfaces are referred to as concave (bends inward ) or convex (bends outward). The topic of infinity comes up when considering a flat surface.
When considering the curved surface of a simple spherical lens, you can imagine that if you drew and followed that curve, your line would eventually reconnect to the initial point you started drawing because the curve represents some segment of a circle of a given radius of curvature. For the case of a flat surface with no curvature, you can imagine this as drawing a straight line. If you were to draw a straight line in one direction, you would never touch the point where you started drawing, thus, it can be considered infinitely curved.
Collimated Plane Wave
In optics, a collimated plane wave can be considered to be coming from infinity. This is a very important principle for optical design. This concept is used for the case of microscopy when considering objective lenses. They are designed to be infinity corrected to enable different combinations of objective and tube lenses or eyepieces.
Using infinity corrected optics allows for engineers to add additional optical elements into infinity space without degrading the image quality. Adding optics to a non infinity corrected microscope will introduce spherical aberrations into the system.