Question

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?

Answer 1

Light takes different amounts of time to travel through different media due to refraction. The time can be calculated by dividing the distance traveled in each medium by the speed of light in that medium.

Step-by-step explanation:

When light travels from one medium to another, it changes direction, a phenomenon called refraction. The time it takes for light to travel from point A to point B in this case can be calculated by dividing the distance traveled in each medium by the speed of light in that medium. In medium 1, the distance traveled is 331 cm and the index of refraction is 1.33. In medium 2, the distance traveled is 151 cm and the index of refraction is 1.51.

Using the equation time = distance / speed, we can calculate the time it takes for light to travel in each medium.

In medium 1: time1 = 331 cm / speed1

In medium 2: time2 = 151 cm / speed2

Answer 2

Answer:
`0.000001475s=1.475\mu s`

Step-by-step explanation:

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

Being its equation as follows:

`n=(c)/(v)` (1)

Where
`c=3(10)^(8)m/s` is the speed of light in vacuum and
`v` 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 :
`v=(c)/(n)` (2)

For medium 1:

`n_(1)=1.33`

`v_(1)=(c)/(n_(1))` (3)

`v_(1)=(3(10)^(8)m/s)/(1.33)=225563909.8m/s` (4)

For medium 2:

`n_(2)=1.51`

`v_(2)=(c)/(n_(2))` (5)

`v_(2)=(3(10)^(8)m/s)/(1.51)=198675496.7m/s` (6)

On the other hand, the velocity
`v` is the distance
`d` traveled in a time
`t`:

`v=(d)/(t)` (7)

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

`t=(d)/(v)` (8)

In this case the total time will be:

`t=t_(1)+t_(2)=(d_(1))/(v_(1))+(d_(2))/(v_(2))` (9)

Where:

`d_(1)=331cm=3.31m` is the distance the light travels in medium 1

`d_(2)=151cm=1.51m` is the distance the light travels in medium 2

`v_(1)=225563909.8m/s` is the velocity of light in medium 1

`v_(2)=198675496.7m/s` is the velocity of light in medium 2

`t=t_(1)+t_(2)=(3.31m)/(225563909.8m/s)+(1.51m)/(198675496.7m/s)` (10)

Finally:

`t=0.000001475s=1.475(10)^(-6)s=1.475\mu s` (10)