A few years ago, Steve Jobs introduced the iPhone 4 with a “retina display” which was so sharp that the human eye couldn’t see make out the pixels. There were no jaggy edges, everything looked like it would in a photograph, a book, or the real world. What they did was cram 960 pixels across a screen that was only about 3 inches across, for a pixel density of 326 pixels per inch (ppi). Later on they introduced a retina display on the iPad and a notebook computer, but there were not as many pixels per inch as the iPhone. The justification for this was that people would hold the iPhone closer to their eyes and the added distance for the iPad and notebook would make the pixels seem just as dense. So in addition to pixels per inch, you also have to take into account the distance to the screen. The Wikipedia article on retina displays say that Apple calls this figure pixels per degree, or PPD (although the article said the PPD does not have a linear relationship with the distance from the eye to the screen, it has since been corrected). Anything with a PPD of 53 or above is considered a retina display.
The new iPad mini does not have a retina display, however it has the same number of pixels as the 10-inch iPad 2, so it is sharper than the non-retina iPad 2. The screen density of the iPad mini is 162 ppi, while the iPad 2 is only 132 ppi. I was thinking about this when considering a Nexus 7 because the Nexus 7 crams a few more pixels than the iPad mini onto a smaller screen. So the Nexus 7 screen has 217 ppi. Taken at a 15-inch viewing distance (the official iPhone distance is 10 inches, though 12 inches is more realistic for me), that comes out to exactly the same PPD value of 57 for the iPhone (or my 4G iPod Touch), though the iPad 3 and iPad 4 with their retina displays have PPD values of 69.
I wanted to play around with this a little more. What about my giant 51-inch HDTV? The HDTV picture has 1080 lines vertically and 1920 pixels across, but the 51 inches is measured diagonally. That comes out to only 25 ppi, but I’m watching it from across the room (140 inches), so it actually comes out to a PPD of 108! Retina Display!
How about my desktop computer’s screen? It has 1024 pixels on a 17-inch screen at a distance of about 22 inches for a PPD of 29. So I can definitely see the pixels at that distance.