The f2.8 of the half-frame lens is used on the half-frame camera to capture the same composition. Is it the same as the f2.8 aperture of a full-frame camera?
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Your "half frame" terminology is incorrect when talking about digital photography. What you mean is " crop frame or sensor". Half frame refers to film era photography. The video below show and explain the digital differences compared to fullframe.
For completeness here is what is meant by half frame in film photography.