The Mirage Distance Measurement · AI Generator #GEN-403B065E
Physics · optics
Problem
A desert surveyor uses an ingenious method to measure distances using mirages. She observes a distant rock formation that appears to have a mirage (inverted image) beneath it due to hot air near the ground. The surveyor's eye is h=1.8m above the ground. She measures that the angle between the direct view of the rock top and the mirage of the rock top is α=0.50mrad (milliradians). The rock formation is H=25m tall. Assuming the mirage forms by total internal reflection at a thin hot air layer just above the ground, and that light rays travel in straight lines except for the single reflection, what is the distance D to the rock formation?