Images are dimensioned in pixels, and screens are dimensioned in pixels, and video systems show pixels directly. This may seem pretty obvious, but the point is, it's very important, because it's how it works, and it's all there is to it, and it's good to know that.
You do need to realize that each of us will see this 500 pixel image width at a different size on our different monitor screens. We don't necessarily see the same thing. On the video screen, we may see the 500 pixel image anywhere between 4 and 8 inches wide, depending on our screen size and settings. My 19 inch 1280x960 pixel CRT screen shows this image as 5.6 inches wide (my 19 inch 1280x1024 pixel LCD screen shows it as 5.8 inches wide). My 17 inch 1024x768 pixel CRT monitor shows it 6.0 inches wide. Most of us will be in that general ballpark, but a 15 inch monitor set to 640x480 pixels may see it at 8 inches wide, or more. A laptop with 1600x1200 pixel display may see it at 4 inches wide, or less. That's a very wide size range for the same image on different screens, and it shows that there is no concept of exact size in inches on the screen. We don't all see the same size on the screen.
So it will be quite necessary to forget about inches on the screen, because video only shows pixels, and screens differ in size. The only one correct answer possible about video image size is that every screen will always see 500 pixels as exactly 500 pixels (assuming we view images at 100% Actual size, otherwise it is about other different pixels). Images are dimensioned in pixels, and screens are dimensioned in pixels, and these 500 pixels will fill 500 pixels on any screen, but those same 500 pixels will fill a different area in inches on different size screens.
so my question still stands....