# How does an afocal lens produce an image on a screen?

I'm really confused about it. If such a lens is necessarily focused at infinity and does not have a plan of focus, then, does it mean it can produce a clear picture on a screen, no matter how close it is to the lens ? Eg., I want to build a telephoto with two positive meniscus (which creates an afocal system), each one having 4000mm of focal length. Then, I would have two questions:

1. How should I calculate what is the resulting focal length ? Would it be halved as it is expected in any focal system with two identical positive lenses ? Like this:

F = (f1 * f2) / (f1 + f2 -d)

Where f1 and f2 are the two lenses' respective focal lengths and D is the space separating them.

1. At what distance should I put my screen from the lens in order to produce a clear picture ? Would there be a certain back focal length ?

Sorry if I can be unclear. I'm an amateur that got really interested in the optics of lenses, and english isn't my native language.

An afocal lens does not produce an image on a screen. Diverging rays from an object or screen point keep diverging on the other side of the lens, just not in a straight continuation. The point of an afocal lens is to change the geometry of the virtual image you are seeing. To get a screen image, you'll still need a convex imaging lens.

Per the wikipedia article for an afocal system d=f1+f2, where d is the distance between the lenses, not the distance to the subject. Your equation then gives F as infinity, saying that you cannot project an image on the screen. In your example you would space the two lenses 8 meters apart and parallel rays coming in would be parallel going out. The lens combination would do nothing except invert the image.

The front focal point of the first lens is imaged at the rear focal point of the second lens... i.e. a subject at infinity would be focused at 4000mm with the two lenses spaced 8000mm apart.

The first image is the typical afocal magnification system w/o consideration of front/rear focal distances.

If instead we consider a subject distant enough to be considered in focus and a point light source (i.e. at infinity) we get the second drawing. Which is then redrawn in the third drawing as an afocal imaging system (w/o focus mechanism). https://spie.org/publications/fg01_p18_afocal_systems