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F-number, just like focal length, does not depend on the sensor size. F-number is the focal length divided by the effective physical aperature diameter. However, since smaller sensors archive the same angle of view at a smaller focal length than larger sensors, then if you have lenses with the same angle of view and f-number, then the aperature diameter of the larger sensor lens will be larger.

("effective" essentialy meaning the size as seen looking through the front of the lens. The actual physical size will be less than the effective size, but it is the effective size that matters -- this correcystic for the placement of the aperature within the lens.)

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