How can a telescope have an f/ratio of f/42?

I was amazed at Jim Melka’s beautiful picture of Mars on page 136 of the January 2006 issue but puzzled by the caption, which said that he used a 12-inch reflector at f/42. How is this possible?

Jim Melka

Jim Melka

Knowing that a telescope’s f/ratio is its focal length divided by its aperture, you’re probably imagining poor Jim wrestling with a 42-foot-long Newtonian. But f/42 is the effective focal ratio of his imaging setup, which includes not only the scope but also a 2× Barlow lens, a filter wheel, and a 16-mm eyepiece that projects a highly magnified image onto his webcam’s CCD chip. The effective focal length of this combination is 12,800 millimeters (504 inches), which, divided by the scope’s 12-inch aperture, gives f/42. With an f/4.2 primary mirror, the scope itself is only a little more than 4 feet long.

— Richard Tresch Fienberg

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