How do waves refract at the boundary of two media?

Waves refract at the boundary of two media by changing direction due to a change in speed.

When a wave travels from one medium to another, the speed of the wave changes, which causes the wave to change direction. This phenomenon is known as refraction. The amount of refraction, or the degree to which the direction of the wave changes, depends on the difference in speed of the wave in the two media.

To understand this, let's consider a wave moving from a medium in which it travels fast (like air) to a medium in which it travels slower (like water). As the wave hits the boundary between the two media, the part of the wave that enters the water first slows down while the rest of the wave is still moving at the original speed. This causes the wave to bend towards the normal line, a line perpendicular to the boundary at the point of incidence.

The change in direction can be predicted using Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocity of the wave in the original medium to the velocity of the wave in the new medium. In mathematical terms, this is expressed as sin(i)/sin(r) = v1/v2, where i is the angle of incidence, r is the angle of refraction, and v1 and v2 are the velocities of the wave in the two media respectively.

Refraction is a fundamental concept in physics and is responsible for many natural phenomena and technological applications. For example, it is the reason why objects appear to be in different positions when viewed through water, why rainbows form, and how lenses in glasses or cameras work. Understanding refraction and how it is affected by the properties of different media is crucial for many areas of physics, from optics to wave theory.