One solution to interstellar space travel that I have heard popularised is to construct a ship with a solar sail and then use a laser to push it away. The advantages are obvious; you don't need to carry any fuel with you, massively reducing the amount of energy needed to thrust.
However, I heard that in the 1960's America wasted billions of dollars trying to develop a system that can intercept an ICBM with a laser. (It just wouldn't work)
Suppose you had colonised the sol system, and had a vast supply of fusion power from readily available gasses. You have a largely roboticised colony in a nearby star system, and you want to transport more human colonists with a continuous thrust of 1 g. (reversing at the half way mark.)
Is there any general law about intercepting projectiles with lasers over vast distances?
Is it viable?