Focal reducers are invaluable for deep-sky work with DSLRs because they make the image smaller and brighter. Since the DSLR sensor is smaller than 35-mm film, you can switch from film to a DSLR, add a focal reducer, and cover the same field with a brighter image.
The most popular Meade and Celestron focal reducers multiply the focal length and f -ratio by 0.63 (giving f /6.3 with an f /10 telescope). That's a handy reduction factor because it shrinks an image from the size of 35-mm film to the size of an APS-C sensor. What's more, the image comes out (1/0.63)2 = 2.52 times as bright, cutting the exposure time to 40% of what it would have been.
But focal reducers are sadly misunderstood, and they don't always work the way the users expect. In what follows, I'll try to clear up some misconceptions.
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