LIGHT RAY FINDS PATH OF LEAST TIME WITHOUT GOOGLE MAP

We know, when a ray of light travels from air to water, it bends according to snell's law. Why should it bend? Why should it follow snell's law?

Say, you are coast guard. Some one cries for help from the sea. You want to reach the person as quickly as possible. Here you have to travel in two media. 1. You have to run in the land (fast). 2. You have to swim in the sea (slow). Hence you need to find the path of shortest time. So you will choose to run a maximum distance on the sand; will reach a particular point on the edge of water; than will swim towards the person in distress.
That path will never be a straight line but looks bent.

Similarly, a ray of light travels faster in air, but slower in water and glass. Hence the light takes a bent path while crossing from air to glass. This is the principle of least time. Also called Fermat's principle.
(Note: When a ray hits a water surface normally (at 90 degree), it will not bend but go straight. (In this case, there is no other path which has 'more least time' than straight line). Next why it should follow snell's law?

sin i/sin r = Refractive index of water = Speed of light in air / speed of light in water- the law
i is angle of incidence and r is angle of refraction as shown in the figure.
The angles depends on the speeds of light in the two media. Hence the speeds determine the angle of bending. Consequently the light ray takes the path of least time.
How the light sense the path of least time? It is because of the wave nature of light. The spherical wave spread from a source of light (a lamp) like a water wave on the sheet of water. These waves senses the nearby paths and finds the quickest path. This principle has been experimentally verified using Radio waves.
There can be many explanations for refraction. This is another way of looking at refraction. Also we get one more idea of 'how the nature works.'

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