18/11/2025
The Mind-Bending Fundamental Reason Why Light Refracts When Passing Through Different Optical Mediums!
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As shown in the attached diagram, we want to predict exactly which path a laser-light beam would take down through point A and the translucent medium beneath it, such that it hits the green line at exactly point B. We will use only the single most fundamental law of physics and the speed of light in each medium to explain fundamentally why the light takes this particular path between the two points.
Upon determining the exact path light should take between the two points, we could then easily determine the correct angle of incidence to shine the light through point A to hit point B and also the angle at which the light refracts when transitioning between the air and the translucent medium along this path. Most importantly, determining why the light travels along this path between the two points will also explain the mind-bending reason why refraction happens in the first place.
Before witnessing the phenomena of refraction, we might initially intuitively wonder that the path a light beam would take that passes through point A and then hits point B, would just be the shortest possible path between the two points, i.e. a straight line between them. After all, whenever light passes through one point in space then hits another point in space while traveling through a single medium (e.g. air), the path the light travels between the two points is always a straight line.
However in our more general case where the light travels through more than one medium that each have a different speed of light to each other, the path light takes through point A that hits point B is not the path that minimizes the travel distance (a straight line), but instead the path that minimizes the total travel time for the light compared to all other hypothetical paths between A and B that the light could have taken!
This logically follows directly from the most fundamental principle behind all physics, the principle of least action, which predicts that in all circumstances objects must always move along the path that minimizes an abstract mathematical quantity closely related to their energy called the object’s action. When the least action principle is applied to the behavior of light passing through mediums, we can use it to derive Fermat’s Principle of Least Time, which logically guarantees that light always follows the path that minimizes its total travel time between any two points, and allows us to precisely calculate what that path would be.
Therefore, astonishingly, because light travels slower through the translucent medium than through the air, the total travel time from A to B would be minimized if the light bends as it enters the slower light-speed medium (as shown on the diagram) so that it travels less distance through the medium with the slower light speed, and so it does, which is the fundamental reason why refraction occurs! The greater the difference in light-speed between the two mediums, the more sharply the light bends downward as it passes into the slower light-speed medium as to always follow the path that minimizes its total travel time between any two points it passes through.
