A light ray enters the Earth's atmosphere and descends vertically through distance h = 100 km to reach the surface. Since the density and composition of the atmosphere vary, its index of refraction also varies as a function of elevation. At the top of the atmosphere, where light enters, the index of refraction is exactly 1.000. At the bottom, where light reaches Earth's surface, the index of refraction is 1.000293. Suppose the refractive index varies linearly between these two values. Calculate the time required for light to travel through the atmosphere. Hint: The definition of velocity v = dx/dt can be written as dt = dx/v = n dx/c. Integrate this expression to find the time. Note that n is not a constant; you must express n as a function of x.

A light ray enters the Earth's atmosphere and descends vertically through distance h = 100 km to reach the surface. Since the density and composition of the atmosphere vary, its index of refraction also varies as a function of elevation. At the top of the atmosphere, where light enters, the index of refraction is exactly 1.000. At the bottom, where light reaches Earth's surface, the index of refraction is 1.000293. Suppose the refractive index varies linearly between these two values. Calculate the time required for light to travel through the atmosphere. Hint: The definition of velocity v = dx/dt can be written as dt = dx/v = n dx/c. Integrate this expression to find the time. Note that n is not a constant; you must express n as a function of x.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter25: Reflection And Refraction Of Light

Section: Chapter Questions

Problem 7OQ: Light traveling in a medium of index of refraction n1 is incident on another medium having an index...

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