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# Statement of a problem № 3987

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Use the concept of optical path to briefly explain why a mirage occurs. Early in the morning, on a sunny day, the heat of the sun produces a thin layer of warm air above the surface of a long straight road. Consider a possible light ray path such as that illustrated in Fig. 15.5. This connects an eye-level point on the tree with an observer of height h = 2 m. If the layer of hot air has refractive index n2 = 1.00020, while the cold air has refractive index n1 = 1.00030. (a) Show that the optical path length along ABCD is approximately n2x + n1sqrt((d-x)^2 + 4h^2) (b) By using Fermat's principle, determine the actual distance that the ray travels in the layer of hot air when d = 500 m. (c) As the observer walks towards the tree, she finds that the mirage disappears. At what distance from the tree does this occur?

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