Bulletin - Vol 8 No. 4 July/August 2005

Pharology 101- Light Visibility

by Denise Shultz, LoA President & Prism Editor

When designing a lighthouse, one of the most important attributes to determine is its range, or how far away the light would still be seen. The maximum distance depends on many factors from the brightness of the light source, the elevation of either the observer or the light, to the state of the atmosphere and the sea. Basically, there are three main factors that influence the visible range of a lighthouse: meteorological visibility, brightness and the geographical range. In the end it is the lesser of these three variables that determines the final visible range.

Meteorological Visibility
The weather conditions at any time can have a dramatic effect on the visibility of a light. It can be either decreased or increased. On one hand, rain, snow, low clouds, fog or smoke can obscure a light to the point of invisibility, whilst on the other hand thermal gradients in the atmosphere create air pockets of different density which act as lenses, refracting the light and making it appear brighter than it actually is, sometimes even making it visible while it is below the horizon. Meteorological visibility is expressed in Nautical Miles (1M=1.8km)

Brightness of the source
Human eye is actually very sensitive to light. It can detect as little as three photons to create a pixel. It's high sensibility is limited to visible light. With wavelengths ranging from 780 to 380 nanometres (one nanometre is one billionth or 10-9 metres) it forms only a very narrow band in the whole spectrum of electromagnetic radiation. This spectrum ranges from low frequency radio waves (longest waves can be several km long) through microwaves (centimetres to millimetres) to infrared (millimetres to micrometres). Then comes the visible light, followed by ultraviolet band (10-7 to 10 -9m), X rays (10-9 to 10-13) and energetic gamma rays (10-10m and shorter). As every secondary school student knows, radiation travels through space at an unimaginably fast speed of 300 000 km/s. 

Nothing in the universe can travel faster without breaking the known laws of physics. Without the optics, the light propagates through space in all directions - on the surface of a sphere. With the use of optics, the light can be concentrated into a specific area. Nevertheless, it still loses its intensity the further it travels from the source, because the same amount of light energy (flux) gets spread on an increasingly large area. This energy loss is governed by an inverse square law E=1/d2 which means that if, for example, the observer moves from the distance of 5 km to the distance of 10 km (or twice as far) the light will appear to be four times fainter than before. Similarly, moving to the distance of 50km (ten times as far) from the light source will see it diminished to 1/100 of its original brightness. 

Ultimately, no matter how bright the initial light source is, given unlimited space and ideal conditions, at certain distance, every light eventually fades even beyond the limit of perception of a very sensitive eye. More so, the intensity of the light decreases faster the further away it travels. Maximum distance the light source can still be seen without taking into consideration other limiting factors is called Luminous Range. Luminous range of the lighthouse is calculated only on the basis of the brightness of the source of its light with the meteorological visibility set at 10 nautical miles (18km). 

Geographic Range
The geographic range is probably the most important limiting factor for a visible range of a lighthouse. Because the earth is a sphere with an average radius (R) of 6378km its surface is slightly curved and its curvature restricts the light's visibility. Two elements limit the geographic range. The height of the light above sea level (h) and the hight of the observer. The higher the light source is positioned, the further away it would be seen. For example (presuming that our observer is at sea level and the conditions are ideal) a light that is elevated 100m above sea level would be seen at a distance of 35.7 km. But if we double the hight of the light to 200m (while the observer stays still at sea level) the geographical range increases less than twice to 50.5 km. Of course the same formula applies to the geographical range of the observer. So, if our observer climbs a cliff 100m high, his 35 km of visible radius will add to the light's geographic range and the distance will double to 71.4 km in the first case and increase to 86.2 km in the second. 

From all the above information, it becomes obvious that a balance between economics and the operational effectiveness has to be found. Increasing the power of the light or its elevation above sea surface does not achieve the equivalent increase in the visible range and a feasible compromise has to be struck. Most very high-powered lights have been abandoned because lights of very great intensity yield diminishing returns in operational effectiveness, though there are still some very high-powered lights which have to be visible at a distance in daylight. In modern beacons a maximum of 100 000 candela with a clear weather range of 20 nautical miles is generally considered adequate.

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