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

Answer: $0.000001475s=1.475\mu s$

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:  

$n=\frac{c}{v}$ (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 : $v=\frac{c}{n}$ (2)

For medium 1:

$n_{1}=1.33$

$v_{1}=\frac{c}{n_{1}}$ (3)

$v_{1}=\frac{3(10)^{8}m/s}{1.33}=225563909.8m/s$ (4)

For medium 2:

$n_{2}=1.51$

$v_{2}=\frac{c}{n_{2}}$ (5)

$v_{2}=\frac{3(10)^{8}m/s}{1.51}=198675496.7m/s$ (6)

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

$v=\frac{d}{t}$ (7)

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

$t=\frac{d}{v}$ (8)

In this case the total time will be:

$t=t_{1}+t_{2}=\frac{d_{1}}{v_{1}}+\frac{d_{2}}{v_{2}}$ (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

$t=t_{1}+t_{2}=\frac{3.31m}{225563909.8m/s}+\frac{1.51m}{198675496.7m/s}$ (10)

Finally:

$t=0.000001475s=1.475(10)^{-6}s=1.475\mu s$ (10)