# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Refraction and dip: a diagram**

**From:**Frank Reed

**Date:**2013 Mar 19, 12:29 -0700

Ten days ago or more, I sketched out a little "cartoon" to explain how dip is altered in a very simple way by refraction (in its simplest form). I didn't get around to posting it then. Maybe it's still relevant to some.

Nearly horizontal light rays are bent downward by refraction in direct proportion to the distance they travel across the Earth's surface. The amount of bending is "k" minutes of arc per nautical mile. If we draw a bunch of light rays from different sources travelling above the curved surface of the Earth, it's a complicated problem to figure out where they're going... But if we take the whole problem, including the curved surface of the Earth, and "un-bend" it by those same "k" minutes of arc per nautical mile, then all the light rays are straight lines and we convert a complicated problem in physics into a simple problem in Euclidean geometry. But it also follows that we have changed the effective curvature of the Earth. We have "un-bent" the Earth's surface. So you can work out any equations for dip and distance by vertical angle, etc. using standard un-refracted geometry and then just replace the radius of the Earth with an "effective radius" of the Earth. That, verbally, is what the diagram shows.

-FER

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