Exact? I've been hearing launch times in the minutes to hours before the probe is too far away to accelerate it enough to be worth while. The problem is laser

Exact? I've been hearing launch times in the minutes to hours before the probe is too far away to accelerate it enough to be worth while. The problem is lasers (on those scales) spread quickly so an ever smaller (even with perfect aiming) fraction of the laser energy will be delivered to the probe. I am curious if the red shift at 1% of the speed of light is enough to throw off the efficiency of the material that's designed for a specific laser frequency. For the same reason the cone of light will be larger than the orbit of any planets around Alpha Centauri. So the exact direction is tough, but that it's heading towards Alpha Centauri is easy. The formula for the angle (in radians) of dispersion: (The laser's wavelength)/(π × The laser's aperture)