Image formed in a compound light microscope I am trying to understand whether the image formed in a compound light microscope is at infinity or not.  I get conflicting answers everywhere I look.
 A: A compound microscope never forms an image at infinity. The image formation is always a variation on the drawing below. For big magnifications, the image position can be quite a long way from the viewer.

What you may be getting confused by is that many (indeed almost all) modern microscopes use infinity conjugate optics. This means that they are made up of two afocal systems placed back to back. Even though I design this stuff part time, you'll have to bear with me as I'm not used to drawing ray diagrams but rather prefer to think of things in terms of waves and Fourier optics. Here's how it works:

The infinite conjugate objective collimates the light from a point source on its object (focal) plane (more strictly, an ellipsoidal focal surface) as shown in the drawing above. So the information in the object plane is encoded in Fourier space as the direction of heading of the plane wave at the innfinity conjugate's output, i.e. it encodes each pixel (diffraction limited point source) on the object plane as a wave vector of a plane wave. A second infinity conjugate system (including the viewer's eye) with its Fourier (afocal) side placed nearest the source inverts this process, i.e. converts the direction of the constituent, collimated plane wave from all the object plane pixels back to pixels (hopefully diffraction limited points) on the viewer's retina (or camera CCD array).
The advantage of doing this is that the distance between the two back-to-back infinity conjugate systems is not critical. It can vary over many centimetres without affecting the system's focus. There is a limit to this variation, but it is not a question of focus. Rather, as the separation between the two infinity conjugates increases, some of the collimated light system misses the aperture of the second lens and vignetting arises. Think of linear superposition (of solutions of Maxwell's equations) and thus consider the effect on a point source. It will beget a plane wave in the Fourier space at some angle to the optical axis. Actually, if it is on axis, no separation between the two infinity conjugate systems will lose light. The further off axis it is, the less separation can be brooked as the more light will be lost.
So, for example, one can simply increase the separation in an infinity conjugate system, put a beamsplitter into the beam path and sample a copy of the light to be directed to cameras and other instruments. It is thus easy to copy and chain many laboratory instruments in an infinity conjugate design.
This is a great improvement over the old, wholly focal compound systems. Typically Zeiss used to use a 160mm focal length where modern systems have afocal Fourier spaces. Some Russian systems (Lomo) used to use 220mm. This length will brook a small variation without too much degradation in system performance, but it is much more critical than an infinite conjugate system and cannot easily have instruments put into the beam path.
