The focal reducer is the opposite of the focal extender: it reduces the equivalent focal length while increasing the brightness of the lens. It's been used for a long time in astronomy. Basically, you take a lens made for full frame and adapt it to the smaller micro 4/3 sensor with a kind of magnifying glass instead of a standard adapter.

EF to micro 4/3 adapter

EF to micro 4/3 adapter

Usually with micro 4/3, if you use a full frame lens, the resulting field of view will be as if you would take that focal length and multiply it by 2. So, for example, a 35mm would have a field of view of a 70mm on a full frame camera. The focal reducer multiplies that by 0.71. It also multiplies the aperture of the lens by the same number. So that 35mm f/1.4 would be equivalent to a 50mm f/1.0 on a micro 4/3 camera. The depth of field is affected by that factor too. Here are some pictures taken with a Bower 35mm f/1.4 and a no-name Focal Reducer.

EDIT: After Samuel's comment, I checked and only shot once into the sun with the lens. I got some flare but not sure if it is from the lens or the focal reducer. In any case, I like the flare that it produces. Two examples:


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