The American Television Systems Committee (ATSC) sets the standards for high-definition television (HDTV). One of the approved HDTV formats is 1080p, which means 1080 horizontal lines scanned progressively (p)—that is, one line after another in sequence from top to bottom. Another standard is 1080i, which stands for 1080 lines interlaced (i). In this system it takes two scans of the screen to show a complete picture: the first scan shows the "even" horizontal lines, the second scan shows the "odd" horizontal lines. Interlacing was the norm for television displays until the 1970s, and is still used in most standard-definition TVs today. Progressive scanning became more popular with the advent of computer monitors, and is used today in LCD, DLP, and plasma HDTVs. In addition, the ATSC sets the standard for the shape of dis- plays. For example, it defines a "wide screen" to be one with a 16:9 ratio; that is, the width of the display is greater than the height by the factor 16/9. This ratio is just a little larger than the golden ratio, 1.618, which is generally believed to be especially pleasing to the eye. Whatever the shape or definition of a TV, the ATSC specifies that it project 30 frames per second on a progressive display, or 60 fields per second on an interlace display, where each field is half the horizontal lines. For the following problems, assume that 1080 horizontal lines are displayed on a television with a screen that is 15.7 inches high (32-inch diagonal), and that the light coming from the screen has a wavelength of 645 nm. Also, assume that the pupil of your eye has a diameter of 5.50 mm, and that the index of refraction of the interior of the eye is 1.36.
a. What is the minimum angle your eye can resolve, according to the Rayleigh criterion and the above assumptions?
b. What is the linear separation between horizontal lines on the screen?
c. What is the angular separation of the horizontal lines as viewed from a distance of 12.0 feet?
d. According to the Rayleigh criterion, what is the closest you can be to the TV screen before resolving the individual horizontal lines? (In practice you can be considerably closer than this distance before resolving the lines.)