Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 34, Problem 46AP

(a)

To determine

Whether an optical day is longer or a geometric day is longer.

(b)

To determine

The difference in the time intervals of optical day and geometric day.

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As sunlight enters the Earth’s atmosphere, it changes direction due to the small difference between the speeds of light in vacuum and in air. The duration of an optical day is defined as the time interval between the instant when the top of the rising Sun is just visible above the horizon andthe instant when the top of the Sun just disappears below the horizontal plane. The duration of the geometric day is defined as the time interval between the instant a mathematically straight line between an observer and the top of the Sun just clears the horizon and the instant this linejust dips below the horizon. (a) Explain which is longer, an optical day or a geometric day. (b) Find the difference between these two time intervals. Model the Earth’s atmosphere as uniform, with index of refraction 1.000 293, a sharply defined upper surface, and depth 8 614 m. Assume the observer is at the Earth’s equator so that the apparent path of the rising and setting Sun is perpendicular to the horizon.
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The index of refraction is defined to be n = A/B where: A = speed of light in material #1 %3D B = speed of light in material #2 OA = speed of light in vacuum B = speed of light in a material A = speed of light in a material B = speed of light in vacuum A = Square root of [(speed of light in vacuum)2 + (speed of light in a material)2] B = speed of light in a material

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Physics for Scientists and Engineers with Modern Physics

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