Skyline horizon from a mountain 130 km away

Abstract

How far is the horizon? A photograph of a city skyline taken from a mountain (elevation 1610 m) at a distance of 130 km is used to introduce the question. The formula that relates the distance to the horizon from an elevated observer is easy to derive when refraction is neglected. The observed horizon distance of the skyline is compared with the theoretical horizon limit of this simple formula. Finally, refraction is discussed and shown to increase the limit by about 10%. A highly interactive component making measurements on Google Maps is included. Introductory students at the high school and first-year college level will find this real-life physics application that incorporates photography, geography, online maps, Earth science, and elementary mathematics very stimulating.