I gauge my distance from the screen by how my eyes focus easily. I don't understand how sonar can determine how well the viewer can see.

It wont determine how well users can see however, it will warn them if they get too close to the screen. To focus easy you should alter the screen resolution and font size not your distance from the monitor.

I feel that a great deal of the modern population has unnecessarily diminished vision, due to television screens and computer monitors. Humans were meant to see with perfect vision, a natural consequence of being outdoors and not focusing long at objects very close to us. Limiting our primary focusing distance by living indoors and using monitors has made many of us nearsighted.

My young nephew has the bad habit of standing a foot away from the television. Any way to instantly "train" him to back away would be a boon to his future eyesight.

I view my monitor at about the same distance that I read a book. I cannot understand what sonar would do to improve that.

I come from an IT background (Education Industry) where every day I see kids ridiculously close to badly configured computer monitors. (Try this for your self. If you have a CRT monitor just set the refresh rate to 60Hertz and work with this setting for a while).This is the reason I had this idea. As well as ensuring users are not too close to the screen this device can detect your computer’s graphics capability and automatically configure your machine with a suitable setting.