Kids everywhere are warned that sitting too close to the TV will ruin their eyesight. Doctors agree that there is no actual evidence that sitting near the screen can cause vision loss. The myth goes back to the early days of TV when some sets emitted X-rays, but that problem has been eliminated.
Sitting too close to the TV can cause eye strain however. The eyes have muscles and over use, by reading or watching TV too close for comfort can cause muscle fatigue. There is little evidence to show that this muscle strain can lead to the need for glasses. It is still best to sit at a distance of a few feet from the screen to prevent discomfort but if your kids insist on sitting closer it is probably not too hazardous.