Derive the law of reflection (Eq. 35.2 ) from Fermat's...

Derive the law of reflection (Eq. $35.2$ ) from Fermat's principle of least time. (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

Fermat's principle of least time states that light travels between two points along the path that requires the least time. This principle is used to derive many optical laws by formulating the travel time as a function of the path and then seeking the conditions under which this function is minimized.

Law of Reflection

The law of reflection, which states that the angle of incidence equals the angle of reflection, can be derived from Fermat's principle. By considering a light ray reflecting off a surface and determining the path that minimizes the overall travel time, one arrives at the conclusion that the reflecting angles must be equal to satisfy the least-time condition.

Calculus of Variations

Calculus of variations is the mathematical technique employed to determine the path that minimizes a certain quantity, such as travel time. In the context of deriving the law of reflection, it involves setting up the time as a function of the point of reflection and then finding the condition where the derivative of this function is zero, leading directly to the result that the incident and reflected angles are equal.

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