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Minimum time fermentation principle. A light ray traveling with speed c leaves point 1, as illustrated in Fig. 1, and is reflected to point 2. The ray strikes the reflecting surface a horizontal distance x from point 1. (a) Show that the time t required for light to travel from 1 to 2 is b) Obtain the derivative of t with respect to x and set it equal to zero to show that time reaches its minimum value when θ1 = θ2 which is the law of reflection and corresponds to the real path followed by light. This is an example of Fermat's principle of least time, which says that, among all possible paths between two points, the one followed by a ray of light is the one for which the travel time is least..

Minimum time fermentation principle. A light ray traveling with speed c leaves point 1, as illustrated in Fig. 1, and is reflected to point 2. The ray strikes the reflecting surface a horizontal distance x from point 1. (a) Show that the time t required for light to travel from 1 to 2 is b) Obtain the derivative of t with respect to x and set it equal to zero to show that time reaches its minimum value when θ1 = θ2 which is the law of reflection and corresponds to the real path followed by light. This is an example of Fermat's principle of least time, which says that, among all possible paths between two points, the one followed by a ray of light is the one for which the travel time is least..

An Introduction to Physical Science
An Introduction to Physical Science
14th Edition
ISBN:9781305079137
Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
Chapter1: Measurement
Section: Chapter Questions
Problem 9MC
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Minimum time fermentation principle. A light ray traveling with speed c leaves point 1, as illustrated in Fig. 1, and is reflected to point 2. The ray strikes the reflecting surface a horizontal distance x from point 1. (a) Show that the time t required for light to travel from 1 to 2 is
b) Obtain the derivative of t with respect to x and set it equal to zero to show that time reaches its minimum value when θ1 = θ2 which is the law of reflection and corresponds to the real path followed by light. This is an example of Fermat's principle of least time, which says that, among all possible paths between two points, the one followed by a ray of light is the one for which the travel time is least..

У1 X 01 02 2 Уг
Transcribed Image Text:У1 X 01 02 2 Уг
t 2 Vy² + x² + √y₂² + (1 − x)² с
Transcribed Image Text:t 2 Vy² + x² + √y₂² + (1 − x)² с
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