Light is refracted as it travels from a point a in medium 1 to a point b in medium 2. if the index of refraction is 1.33 in medium 1 and 1.51 in medium 2, how much time does it take for light to go from a to b, assuming it travels 331 cm in medium 1 and 151 cm in medium 2?

Explanation:

The index of refraction is a number that describes how fast light propagates through a medium or material.  

Being its equation as follows:  

(1)

Where is the speed of light in vacuum and its speed in the other medium.

So, from (1) we can find the velocity at which the light travels and then the time it requires to travel : (2)

For medium 1:

(3)

(4)

For medium 2:

(5)

(6)

On the other hand, the velocity is the distance traveled in a time :

(7)

We can isolate from (7) and find the value of the required time:

(8)

In this case the total time will be:

(9)

Where:

is the distance the light travels in medium 1

is the distance the light travels in medium 2

is the velocity of light in medium 1

is the velocity of light in medium 2

(10)

Finally:

(10)

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