# Lighthouses: Do Freznel lenses defy trig? **URL:** \ **Category:** Factual Questions\ **Created:** [November 27, 2002, 11:02pm UTC](https://boards.straightdope.com/t/lighthouses-do-freznel-lenses-defy-trig/139237 "2002-11-27T23:02:31Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [November 27, 2002, 11:02pm UTC](https://boards.straightdope.com/t/lighthouses-do-freznel-lenses-defy-trig/139237/1 "2002-11-27T23:02:31Z")
Many books on lighthouses will state how tall a lighthouse stands above the water (tower + elevation above sea level). Then, they’ll say how far out to sea the beacon can be seen. More precisely, books will sometimes give the height of the focal plane above sea level. However, using basic trig, I cannot confirm their numbers which seem quite exaggerated compared to mine…regarding how far the light can be seen out to sea. I can only WAG to ask: Does the Freznel lens (of various designs) broaden the light beam so that 1/2 the beam rises significantly higher than the focal plane - the further the light gets from the source - thus projecting the light higher, and granting more visibilty from a greater distance? If you like, I can show you my figs. for I used trig to figure out the distance to the horizon. But, did I over-simplify the problem? I wonder if any other SDoper has given this any thought? - Jinx ---
**Author:** ![Turbo\_Dog](https://avatars.discourse-cdn.com/v4/letter/t/ce73a5/32.png) [@Turbo\_Dog](https://boards.straightdope.com/u/Turbo_Dog)\ **Post date:** [November 27, 2002, 11:33pm UTC](https://boards.straightdope.com/t/lighthouses-do-freznel-lenses-defy-trig/139237/2 "2002-11-27T23:33:20Z")
[Here](http://www.howstuffworks.com/framed.htm?parent=question244.htm&url=http://www.lanternroom.com/misc/freslens.htm) it says that a lens 100’ above sea level has a visible range of about 18 miles. ---
**Author:** ![Finagle](https://avatars.discourse-cdn.com/v4/letter/f/b19c9b/32.png) [@Finagle](https://boards.straightdope.com/u/Finagle)\ **Post date:** [November 27, 2002, 11:42pm UTC](https://boards.straightdope.com/t/lighthouses-do-freznel-lenses-defy-trig/139237/3 "2002-11-27T23:42:44Z")
Well, you could check your math – a rule of thumb is that the distance to the horizon in nautical miles is roughly the square root of the height of the object in feet. So a 100 foot lighthouse should be visible at about 10 nautical miles (11 1/2 miles, more or less). ---
**Author:** ![Turbo\_Dog](https://avatars.discourse-cdn.com/v4/letter/t/ce73a5/32.png) [@Turbo\_Dog](https://boards.straightdope.com/u/Turbo_Dog)\ **Post date:** [November 27, 2002, 11:49pm UTC](https://boards.straightdope.com/t/lighthouses-do-freznel-lenses-defy-trig/139237/4 "2002-11-27T23:49:40Z")
You also have to factor in the height of the person aboard a ships deck or crows nest viewing the light, not just the light itself. ---
**Author:** ![Turbo\_Dog](https://avatars.discourse-cdn.com/v4/letter/t/ce73a5/32.png) [@Turbo\_Dog](https://boards.straightdope.com/u/Turbo_Dog)\ **Post date:** [November 28, 2002, 12:00am UTC](https://boards.straightdope.com/t/lighthouses-do-freznel-lenses-defy-trig/139237/5 "2002-11-28T00:00:21Z")
deck height on an average clipper in the mid 1800’s is about 25 feet give or take. The big ones had main masts over 200 feet. A guy in a crows nest on a clipper could then conceivable see a lighthouse beam at 40 to 50 nmi. What numbers are you looking at that seem exagerrated, **Jinx**? ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [November 28, 2002, 12:42am UTC](https://boards.straightdope.com/t/lighthouses-do-freznel-lenses-defy-trig/139237/6 "2002-11-28T00:42:03Z")
> [@](#): > > \*Originally posted by Turbo Dog \* > \*\*deck height on an average clipper in the mid 1800’s is about 25 feet give or take. The big ones had main masts over 200 feet. A guy in a crows nest on a clipper could then conceivable see a lighthouse beam at 40 to 50 nmi. > > What numbers are you looking at that seem exagerrated, **Jinx**? \*\* Let me re-run the numbers, and see if it’s in keeping with all that’s been stated here…I’ll repost ASAP, but the holiday weekend may delay how soon I can come back to post a reply… Thanks for your patience… - Jinx ---
**Author:** ![astro](https://avatars.discourse-cdn.com/v4/letter/a/9dc877/32.png) [@astro](https://boards.straightdope.com/u/astro)\ **Post date:** [November 28, 2002, 1:03am UTC](https://boards.straightdope.com/t/lighthouses-do-freznel-lenses-defy-trig/139237/7 "2002-11-28T01:03:55Z")
[Procedure for computing the visibility of a light](http://www.swos.navy.mil/doc/CP%20I/Module%207/Student%20Guide/Information%20Sheets/Is7-04.doc) > [@](#): > > a.Compute the horizon distances for you and the geographic range for the light. > > b. Compute the luminous range of the light based on the nominal range of the light and the prevailing visibility by using the luminous range diagram. See figure 5A-13-5. > > c.Compare values from steps a and b. The computed visibilty is the lesser of the two. > > Example 1: Determine the visibility of light Alpha for an observer with a height of eye of 50 feet. The visibility of the day is 5.5 miles. > > Solution: From the Light List, the nominal range is determined to be 20 miles; the height of light Alpha is 90 feet above the water. > > Determine horizon distance from figure 5A.13.3. > > Height of eye for 50 feet 8.3 miles > Height of light (90 feet) 11.1 miles > Computed range 19.4 miles > Nominal range 20.0 miles > Luminous range 13.0 miles > Computed Visibility 13.0 miles (in this case, luminous range\ [@](#): > > How far away you can see a light depends not only on your height, the object’s height, and atmospheric clarity, but also on the strength of the beam of light. Different terms are used to sort these factors. > > Luminous range is the maximum distance at which a light can be seen as determined by the intensity of the light and the meteorological visibility prevailing at the time; it takes no account of height. > > Nominal range is the luminous range when visibility is unlimited. > > Geographic range is the maximum distance at which a beam of light can theoretically reach an observer, as limited only by the height of the light and the refraction of the atmosphere. Geographic ranges assume a height of eye of 15 feet (about 5 meters). > > The Lights Rising and Dipping Table on is based on normal atmospheric refraction and should not be used when conditions are abnormal. The range shown on charts of U.S. waters is the nominal range. All heights of lights are given above high water. Allowance for the state of the tides should be made with lights of small elevation. > > Glare from background lighting reduces considerably the range at which lights are sighted. A light of 100,000 candle power has a nominal range of about 20 miles; with minor background lighting, as from a populated coastline, this range is reduced to about 14 miles; and with major background lighting, as from a city or from harbor installations, to about nine miles. > > Navigators with a near horizon and using the powerful lights around the U.S. coastline will probably be more concerned with the geographic range of lights. Vertical Sextant Angle.