Road mirage angle

Abstract

A video is taken of a roadsign mirage from the passenger seat in a car traveling at constant speed on a highway. The video spans the duration of seeing the mirage of the sign, viewing the vanishing of the mirage as the car approaches, and passing the road sign. The mirage angle, defined as the angle with respect to the horizontal at the moment the observer notes the vanishing of the mirage, can be determined from the video, the speed of the car, and known dimensions of the standard road sign. The value can be checked with a theoretical formula using the ambient weather temperament and consulting references to determine the temperature of the air in contact with the road surface. Agreement between observation and theory is within the error bounds. In the conclusion, a quick observational estimate is made in the car without needing the video.

Skyline horizon from a mountain 130 km away

“…In this case the change in index refraction 'due to pressure drop with height is just compensated by the accompanying temperature drop' [19] and the light does not refract. Large temperature gradients near hot road surfaces produce negative curvatures (k < 0) causing light from objects and the sky to curve upward to the observer, who then perceives that water is up ahead on the road, an inferior mirage [20].…”