Sir/madam,
When we talk about refraction we say that light wants to take the quickest path to reach a point and therefore it bends accordingly while entering in a different medium; but light does not wants to reach any particular point, it just wants to travel forever:how do we justify this?
Sir/madam,
When we talk about refraction we say that light wants to take the quickest path to reach a point and therefore it bends accordingly while entering in a different medium; but light does not wants to reach any particular point, it just wants to travel forever:how do we justify this?
There is a principle in optics called Fermat's principle of least time, which states that light will travel along a path between two points that represents the path of least time. This is an application of a more general principle, known at the principle of least action, which was loved by Physicists, such as Feynman, because it can provide a convenient route towards working out complex dynamics. It's the basis behind Feynman's path integral formalism of quantum electrodynamics, and is also widely used in working on problems in General relativity. So it's a very powerful approach.
With respect to optics, it's quite straight forward: Light will take the path of least time between two points. That even seems reasonable to our intuition. Why would light want to dawdle along a different path, even if the path is geometrically shorter? Light needs to get where it's going as fast as it can.
If the two points happen to lie within different media, with different refractive indices, then the path of least time might not be straight. It's not so hard to see why this must be so:
Firstly, in a homogeneous medium, the shortest path between two points will be a straight line. So we are happy with this.
Now consider one point in air and another in water. Light travels slower in water than it does in air, so if it's at all possible, light will travel along a path that minimises the time in the water (where it travels slower). If the two points are connected by an imaginary line that is perpendicular to the surface separating the two media, then it will travel along that straight line. Any deviation from that path will mean it takes a longer path in water AND a longer path in air. The fact that any deviation from a straight line will results with a longer time spent in water means that no other path can be the path of least time in this case.
However, if the imaginary line between the two points is NOT perpendicular to the surface of the water, it is possible that a path that deviates from the straight line will involve a shorter path in the water AND a longer path in air. Because water is the slower medium, you can minimise the time of flight by minimising the time spent within the water. Therefore, a faster path will be one where the light spends less time in the water. If you scribble this down on a piece of paper, you can immediately see that the faster path will have light bending towards the direction normal (perpendicular) to the surface, which is exactly what we expect from refraction
There is a principle in optics called Fermat's principle of least time, which states that light will travel along a path between two points that represents the path of least time. This is an application of a more general principle, known at the principle of least action, which was loved by Physicists, such as Feynman, because it can provide a convenient route towards working out complex dynamics. It's the basis behind Feynman's path integral formalism of quantum electrodynamics, and is also widely used in working on problems in General relativity. So it's a very powerful approach.
With respect to optics, it's quite straight forward: Light will take the path of least time between two points. That even seems reasonable to our intuition. Why would light want to dawdle along a different path, even if the path is geometrically shorter? Light needs to get where it's going as fast as it can.
If the two points happen to lie within different media, with different refractive indices, then the path of least time might not be straight. It's not so hard to see why this must be so:
Firstly, in a homogeneous medium, the shortest path between two points will be a straight line. So we are happy with this.
Now consider one point in air and another in water. Light travels slower in water than it does in air, so if it's at all possible, light will travel along a path that minimises the time in the water (where it travels slower). If the two points are connected by an imaginary line that is perpendicular to the surface separating the two media, then it will travel along that straight line. Any deviation from that path will mean it takes a longer path in water AND a longer path in air. The fact that any deviation from a straight line will results with a longer time spent in water means that no other path can be the path of least time in this case.
However, if the imaginary line between the two points is NOT perpendicular to the surface of the water, it is possible that a path that deviates from the straight line will involve a shorter path in the water AND a longer path in air. Because water is the slower medium, you can minimise the time of flight by minimising the time spent within the water. Therefore, a faster path will be one where the light spends less time in the water. If you scribble this down on a piece of paper, you can immediately see that the faster path will have light bending towards the direction normal (perpendicular) to the surface, which is exactly what we expect from refraction
