Question

Consider a common mirage formed by superheated air immediately above a roadway. A truck driver whose eyes are 2.00 m above the road, where n = 1.000 293, looks forward. She perceives the illusion of a patch of water ahead on the road. The road appears wet only beyond a point on the road at which her line of sight makes an angle of 1.34° below the horizontal. Find the index of refraction of the air immediately above the road surface. (Treat this as a problem in total internal reflection. Give your answer to six significant figures.)

Answer 1

1.00002

Step-by-step explanation:

`\theta_r` = Angle of refraction = 90°

`\theta_i` = Angle of incidence = (90-1.34)°

`n_i` = Refractive index of incident air = 1.000293

`n_r` = Index of refraction of the air immediately above the road surface

Mirages occur at the critical angle

We have the relation

`n_isin\theta_i=n_rsin\theta_r\\\Rightarrow n_r=(n_isin\theta_i)/(sin\theta_r)\\\Rightarrow n_r=(1.000293* sin(90-1.34))/(sin90)\\\Rightarrow n_r=1.00002`

The index of refraction of the air immediately above the road surface is 1.00002