What is the name of the relationship (Sin a)/(Sin B)=(V1)/(V2) between the incident and refracted angles and wave speeds?

• A. Snell's Law
• B. Fermat's Principle
• C. Boyle's Law
• D. Snell's Principle

Answer: (A)

This relation describes how waves bend when moving from one medium to another with a different speed. At the boundary, the wavefronts must align so that the tangential part of the wave’s phase stays continuous, which leads to a specific link between the incident and refracted angles and their speeds. Since the wavevector magnitude is inversely related to speed, the continuity condition gives sin a / sin B = V1 / V2. This is Snell's Law, often written as sin θ1 / sin θ2 = v1 / v2 or n1 sin θ1 = n2 sin θ2. Here a and B are the angles to the boundary normal, and V1 and V2 are the speeds in the first and second media. It explains why the ray bends toward the normal when entering a slower medium and away from the normal when entering a faster one. (Fermat's Principle deals with the path of least time, and Boyle's Law concerns gas behavior, so they don't describe this specific relationship.)