In a number of applications the high precision microscopes are indispensable and rather complex instruments, which have afocal optical systems. The magnification of afocal optical systems is independent of the object distance. Therefore we can form a real image with a constant height of an object from a comparatively big object distance range . Our aim is to develop an afocal optical system with a relatively big numerical aperture that facilitates the description of the vectorial calculation of electromagnetic field propagation from the object to the image . The preconditions of these vectorial calculations will be achieved by a complex rear and a single front elements special afocal optical system, of which the following are strictly true: The object is in the front focal plane of the front element, the image is in the rear focal plane of the rear element, the aperture stop is in the rear focal plane of the front element and in the front focal plane of the rear element on the adjacent coincidental focal planes. Consequently, the raytracing is telecentrical in both the object and image space. The presentation shows the design of the afocal optical system that satisfies the above conditions and specifications.