Light follows the path of least distance, known as Fermat's principle or the principle of least time, due to its wave-like nature and the way it interacts with its surroundings. This principle was first formulated by the French mathematician and physicist Pierre de Fermat in the 17th century.
According to Fermat's principle, light takes the path that minimizes the time it takes to travel between two points. This principle can be explained by considering the wave nature of light. Light waves propagate through a medium or space, and they can be described by their wavefronts, which are surfaces of constant phase.
When light travels from one point to another, it encounters different media or objects that can change its speed. In homogeneous media, such as air or vacuum, light travels in straight lines. However, when light passes through media with varying refractive indices, such as air and water or different layers of the atmosphere, its speed and direction can change.
The speed of light in a medium is inversely proportional to the refractive index of that medium. As light crosses the boundary between two media with different refractive indices, it bends or changes direction. This phenomenon is called refraction.
When light travels between two points, it can take multiple paths, each with a different distance and time of travel. According to Fermat's principle, light will choose the path that minimizes the time taken to reach its destination. This is because light waves interfere with each other, and the path that takes the least time corresponds to constructive interference, where the crests and troughs of the waves align to reinforce each other.
In other words, if there are multiple paths that light can take, the path with the shortest distance will result in the least time taken, and therefore, it is the path that light tends to follow. This principle is consistent with observations and is a fundamental concept in optics.