The upper limit on angular resolution for the human eye is about 0.008 degrees, based on the Rayleigh diffraction limit for light entering the pupil. The binocular, central field of view is about $60^\circ$ vertically and $120^\circ$ laterally, so if you divided that up into the smallest cells it would be possible to resolve with human-sized pupils, you'd get about 112 million "pixels."
Of course, human eyes don't work nearly that well, so this is just an upper limit. Most humans have a visual acuity which allows them to distinguish objects separated by about 1 arc minute, or about $0.016^\circ$ - twice the diffraction limit, which would mean only about 28 million "pixels."
I'm not really sure what you mean about finding a physical way to obtain an answer. If you mean you want to measure somebody's visual acuity - that is, the smallest angular separation they can resolve - then optometrists do that every day. It's also worth noting that eyes don't have pixels, and that angular resolution depends on where in the visual field the objects are located, lighting conditions, etc.