I've drawn you below a very crude rendition of the situation, which isn't to scale, but should hopefully give you an idea:

Purple dot = lighthouse
Purple circle = lighthouse 3km radius (safe zone)
Red circle = Ellethia area where life/death cycle continues (this should technically be around the entire coast line, not just the lighthouse area, but it's harder to draw on this laptop pad)

The distance between the purple and red circles should not be that small, this is just indicative.

Green dots = mermaids
Grey line = mist
Brown dots = boats