Full-frame v. DX Viewfinder Brightness

On a photography forum somewhere (I’m sorry, I’ve lost track of it), I saw the following comment:

“In this regard, once again, your f/2.8 lens is “slow” in that it cannot illuminate a viewfinder as large as a FF viewfinder as brightly.”

This seems highly suspicious to me. The physics of optics uses f/ values as estimated measures of light-gathering capability. To a first approximation, they also serve as highly correlated measures of light transmittance. (Lots of elements in a lens design will factor in a reduction in transmittance, and thus the T-stop for critical exposure and reproduction work.) The amount of light transmitted per unit area in the focal plane is exactly the same for the same f/2.8 lens mounted on a DX camera, on an FX camera, or even on an oatmeal box, and will be quite similar even for different lenses of maximum f/2.8 aperture. Modulo some minor concerns about light fall-off with a larger image circle, the absolute amount of light per unit area in the viewfinder remains a constant for any lens shared between DX and FX bodies.

The expectation, in fact, would be that DX bodies will have apparently dimmer viewfinders, or if equally bright, that the DX viewfinder image will subtend a smaller apparent angle. Magnifying the smaller DX viewfinder image area to subtend the same apparent angle of view as the FX viewfinder image area will necessarily deliver a smaller amount of light per unit area to the retina (assuming the viewfinders are constructed using the same materials in each case and differ only in the optics).

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