Why does refraction happen? That is, what is the physical reason a wave moves in a new medium with a different velocity than it did in the original medium?

Snell's Law is a fundamental concept in wave optics that explains how a wave, such as light or sound, bends, or refracts, when it travels from one medium to another with a different refractive index. This law is mathematically expressed as:
\( n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \)
where \( n_1 \) and \( n_2 \) represent the refractive indices of the original and new medium, respectively, and \( \theta_1 \) and \( \theta_2 \) are the angles of incidence and refraction. The refractive index is a dimensionless number that describes how light propagates through that medium compared to the speed of light in a vacuum.
Snell's Law is critical for understanding phenomena like the bending of a straw in water or the splitting of light into a rainbow by a prism. The ability to calculate the change of angle can also help in designing lenses for glasses and cameras to ensure proper light direction and focus.

Huygens' Principle lays the groundwork for understanding wave phenomena including refraction, reflection, diffraction, and interference. It proposes that every point on a wavefront is a source of spherical secondary wavelets, which spread out in the forward direction at the speed characteristic to that medium. After a certain amount of time, the new position of the wavefront is the tangential surface to these secondary wavelets.
Applying Huygens' Principle to Refraction
When dealing with refraction, Huygens' Principle helps to visualize how a planar wavefront changes as it crosses the boundary between two media with different wave velocities. The secondary wavelets in the slower medium will lag behind those in the faster medium, causing the wavefront to bend at a different angle, as predicted by Snell's Law. This principle is fundamental not just in theoretical studies but also in practical applications like the creation of holograms and understanding seismic wave propagation.

The refractive index, often denoted as \( n \), is a measure that indicates how much the speed of light is changed when it enters a material. A higher refractive index indicates that light travels slower in that medium compared to a medium with a lower refractive index. The refractive index of a vacuum is 1, and air is approximately 1.003, which are used as reference points.
Refractive index and optical materials
Materials with varying refractive indices are selected for lenses and other optical devices based on desired light-bending properties. For example, a material with a high refractive index will bend light more than one with a lower refractive index, which is a principle exploited in corrective eyewear and photography. Understanding this concept is essential in designing a multitude of optical devices and in studying the behavior of light in different environments.

Wave velocity is the speed at which a wave propagates through a medium. This speed can be affected by the medium's physical properties, such as its elasticity, density, and temperature. For example, sound waves travel faster in solids than in liquids, and even faster in gases, because of the differences in these properties.
Factors affecting wave velocity
While elasticity tends to increase wave speed, higher density typically reduces it. In the context of light, the velocity depends on the optical density of the medium and is inversely proportional to the refractive index. Light, therefore, travels at its maximum speed in a vacuum, with the velocity in any other medium being a fraction of this.
Understanding wave velocity is crucial not only in basic physics but also in diverse fields like meteorology, oceanography, and telecommunications, where the transmission and interpretation of waves are fundamental to operations.