Answer: [tex]0.000001475s=1.475\mu s[/tex]
Explanation:
The index of refraction [tex]n[/tex] is a number that describes how fast light propagates through a medium or material.
Being its equation as follows:
[tex]n=\frac{c}{v}[/tex] (1)
Where [tex]c=3(10)^{8}m/s[/tex] is the speed of light in vacuum and [tex]v[/tex] 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 : [tex]v=\frac{c}{n}[/tex] (2)
For medium 1:
[tex]n_{1}=1.33[/tex]
[tex]v_{1}=\frac{c}{n_{1}}[/tex] (3)
[tex]v_{1}=\frac{3(10)^{8}m/s}{1.33}=225563909.8m/s[/tex] (4)
For medium 2:
[tex]n_{2}=1.51[/tex]
[tex]v_{2}=\frac{c}{n_{2}}[/tex] (5)
[tex]v_{2}=\frac{3(10)^{8}m/s}{1.51}=198675496.7m/s[/tex] (6)
On the other hand, the velocity [tex]v[/tex] is the distance [tex]d[/tex] traveled in a time [tex]t[/tex]:
[tex]v=\frac{d}{t}[/tex] (7)
We can isolate [tex]t[/tex] from (7) and find the value of the required time:
[tex]t=\frac{d}{v}[/tex] (8)
In this case the total time will be:
[tex]t=t_{1}+t_{2}=\frac{d_{1}}{v_{1}}+\frac{d_{2}}{v_{2}}[/tex] (9)
Where:
[tex]d_{1}=331cm=3.31m[/tex] is the distance the light travels in medium 1
[tex]d_{2}=151cm=1.51m[/tex] is the distance the light travels in medium 2
[tex]v_{1}=225563909.8m/s[/tex] is the velocity of light in medium 1
[tex]v_{2}=198675496.7m/s[/tex] is the velocity of light in medium 2
[tex]t=t_{1}+t_{2}=\frac{3.31m}{225563909.8m/s}+\frac{1.51m}{198675496.7m/s}[/tex] (10)
Finally:
[tex]t=0.000001475s=1.475(10)^{-6}s=1.475\mu s[/tex] (10)
