From the scientific point, the children who watch TV or play computer are easier to have vision problems compared with others, which means, the longer they get in touch with TV or computer, the more possible their eyes will be harmful due to a long time radiation. There is a professional explanation, too many radiations are absolutely damage to our eyes, and will give rise to the changes of our retina's radian. At the end, Accordingly, as far as i am concerned, it's totally no problems allowing them to enjoy their free time, but moderating in the time is also necessary in consideration of your kid's eyes. even lead to myopia or other vision problem.
Well, it seems that you concern quite a lot about your kids' health. Yes, of course, by watching too much TV shows, it would be harmful to the eyes of the children, because long time of exposure to the TV screen, the eyes will take in some harmful lights and radiation, which would damage the eyes to some extent. So, it would be best for the kids to take breaks at intervals and relax their eyes.
It is very bad for the kids to see too much tv or the computer which will cause the short sighted symptom. Yes, the screen is really harmful for the kid's eyes. When you look at the screen at so near distance, your visual nerves will be damaged which will cause the tiredness easily. Thus, you'd better leave some distance between the screen and your eyes.