Answer to Question #268965 in Optics for sai

Question

Mirage. The figure below shows a simplified situation of a mirage. The air is

stratified into three layers with refractive indices ni with i = 1, 2, 3. The continuous

variation of refractive index with height on a hot day is similar for n3 > n2 > n1.

The bottom two layers have a thickness of a and b, respectively. An observer

at height h is looking at a tree of height H. Calculate the minimum horizontal

distance between the tree and the observer so that the observer sees a mirage. Take

n3 = 1.01, n2 = 1.02, n3 = 1.03, a = b = 0.5 m, h = 2 m, and H = 10 m.

Answer 1

${n1=1.01}\\{n2=1.02}\\{n3=1.03}\\ {sin\theta=\frac{n1}{n2}=\frac{n2}{n3}}\\ {\theta=sin^1{(\frac{n1}{n2})}}\\ {\theta=sin^1{(\frac{1.01}{1.02})}}\\ {\theta=81.97}\\ {Tan\theta=\frac{opposite}{Adjacent}}\\ {Horizontal\,Distance=\frac{9}{Tan81.97}}\\ {Horizontal\,Distance=1.27m}$