Celestron’s focal reducer/corrector is optimized to change the focal ratios and effective focal lengths of f/10 Schmidt-Cassegrain telescopes (SCTs).
A focal reducer is an accessory that screws onto the threads on the back of your SCT’s optical tube assembly (OTA) to give a smaller and brighter image at prime focus. It yields lower magnifications, a wider field of view and a faster photographic f-number than the original f/10 configuration of the OTA. To do this, it shortens the converging cone of light from the main optics, bringing the focal plane closer to the back of the telescope. There will be vignetting at the lowest powers or for prime focus photography.
Optically, focal reducers (also called telecompressors) are positive lenses of two or more elements described in terms of the magnification factor. Celestron makes a focal reducer that has a magnification factor of 0.63. (Since this number is less than one for reducers, it's often called the compression factor.) The resulting f-number with the reducer on the scope for a SCT that has f/10 optics is this factor times the f-number, f/6.3. This reducer is often called the f/6.3 focal reducer.
However, the actual degree of compression is dependent on the spacing of the lens from the eyepiece or camera image plane. The compression is less (higher effective f-numbers) for short distances, greater (smaller f-numbers) for longer distances.
For the Celestron reducer with a focal length of 231mm working at f/6.3, the spacing is 105 mm. For Celestron accessories simply screw the reducer onto your scope and view at f/6.3. For aftermarket uses the compression ranges from about 0.7 at 50 mm spacing to about 0.5 at 225 mm spacing.