The telescope produces a real image some distance behind the rear plate of the telescope. This real image is normally viewed with an eyepiece or intercepted by a photographic film or CCD imager. For objects at infinity, like stars, this image can be moved closer to or farther from the back plate by moving the mirror. This is called focussing. As the mirror is moved back, the real image moves closer to the back plate and as the mirror is moved forward toward the secondary, the image moves farther away from the back plate.
Focal reducers are positive lenses which do two things to the real image.
It is the reduced image that is desired since it is both smaller and brighter. Thus more image fits on the film or CCD imager, which has the effect of decreasing the effective focal length of the telescope. It also increases the surface brightness of the real image thus decreasing the effective f number of the telescope. Focal reducers are designed, optically, to work at a fixed and specified distance from the film or CCD imager. They are best corrected for this one distance.