Q: How do we know what luminous intensity to use in a lighthouse?
Remember that the Earth is curved, so, as long as the light reaches the horizon, that ought to be sufficient: light, travelling in straight lines, can only be seen beyond the horizon by adding height either to the light source or to the observer. The visibility of a light is determined not just by the distance to the horizon but by the height of the light above the surface of the Earth. Thus, a light on a high point of land can be seen at a greater distance than a light close to sea level. What these two things mean is that, if you have a light at sea level, it can be seen at a distance to the horizon of, say, twelve miles (18 Km) and a light of 250,000 candle-power is sufficient to be seen at that distance. However, if you have a light on a high point of land, say, 300 feet (100 m), it could be seen at a distance to the horizon of 25 miles (40 Km) and a light of greater intensity, say, 1 million candle power, is necessary to cover the greater distance.