I'm not sure if monitors cause eye "damage" but you can certainly get eyestrain from them. I'm not sure that getting an LCD will reduce eyestrain either. From what I've seen of them, I find them quite a bit harder to look at than CRT's.
But for what it's worth, here's my hint on reducing eyestrain: get the biggest monitor you can afford, then set it back to a position that is as far as possible from your face but which still enables you to comfortably read the text. This makes the monitor smaller in your overall field of vision in relation to the surroundings, ie you are not getting so saturated with light from an artificial light source.
Also, make sure no ambient light is falling on the monitor face because this makes the screen harder to see. If there is a natural light source in the room, ie window, try to have the monitor facing away from it rather than toward it so you don't get reflective glare. Ditto for any artificial light source in the room if possible.
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