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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.)

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boffeemadrid

Answer:

1.00002

Explanation:

[tex]\theta_r[/tex] = Angle of refraction = 90°

[tex]\theta_i[/tex] = Angle of incidence = (90-1.34)°

[tex]n_i[/tex] = Refractive index of incident air = 1.000293

[tex]n_r[/tex] = Index of refraction of the air immediately above the road surface

Mirages occur at the critical angle

We have the relation

[tex]n_isin\theta_i=n_rsin\theta_r\\\Rightarrow n_r=\frac{n_isin\theta_i}{sin\theta_r}\\\Rightarrow n_r=\frac{1.000293\times sin(90-1.34)}{sin90}\\\Rightarrow n_r=1.00002[/tex]

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

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