Question

Derive the law of reflection (Eq. 35.2$)$ from Fermat's principle. (See the procedure outlined in Section 35.9 for the derivation of the law of refraction from Fermat's principle.)

Name: Problem 65, Chapter 35: Physics for Scientists and Engineers with Modern Physics
Uploaded: 2021-07-04T15:19:58-08:00
Duration: 2 min 58 s
Channel: Keshav Singh
Description: Derive the law of reflection (Eq. 35.2) from Fermat's principle. (See the procedure outlined in Section 35.9 for the derivation of the law of refraction from Fermat's principle.)

   Derive the law of reflection (Eq. 35.2$)$ from Fermat's principle. (See the procedure outlined in Section 35.9 for the derivation of the law of refraction from Fermat's principle.)

Physics for Scientists and Engineers with Modern Physics

Paul Tipler, Gene… 6th Edition

Chapter 35, Problem 65

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Solved by Expert Keshav Singh

07/04/2021

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This principle can be used to derive the laws of reflection and refraction. Show more…

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Derive the law of reflection (Eq. 35.2$)$ from Fermat's principle. (See the procedure outlined in Section 35.9 for the derivation of the law of refraction from Fermat's principle.)

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Key Concepts

Fermat's Principle

This principle states that the path taken by a ray of light between two points is the one which requires the least time, or more generally, an extremum of the travel time. It is fundamental in optics as it explains the behavior of light, including reflection and refraction, through a variational approach.

Law of Reflection

The law of reflection establishes that when light reflects off a surface, the angle of incidence is equal to the angle of reflection. This law can be derived by applying Fermat's principle, as the optimal path that minimizes the optical path length naturally leads to this equality of angles.

Calculus of Variations

The calculus of variations is a mathematical framework used to find functions that minimize or maximize functionals. In the context of optics, it is employed to derive the conditions under which the travel time of light is stationary, leading directly to results like the law of reflection.

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