1. Speed of light in the material: [tex]1.75\cdot 10^8 m/s[/tex]
The speed of light in a material is defined as follows:
[tex]v=\frac{d}{t}[/tex]
where
d is the distance travelled by light in the material
t is the time taken
In this problem, we have
[tex]d=875 km = 8.75\cdot 10^5 m[/tex] is the distance travelled in the material
[tex]t=5.00 ms=0.005 s[/tex] is the time taken
So, the speed of light in the material is
[tex]v=\frac{8.75\cdot 10^5 m}{0.005 s}=1.75\cdot 10^8 m/s[/tex]
2. Index of refraction: 1.71
The index of refraction of a material is defined as:
[tex]n=\frac{c}{v}[/tex]
where
[tex]c=3.00\cdot 10^8 m/s[/tex] is the speed of light in a vacuum
v is the speed of light in the material
For this material, we have
[tex]v=1.75\cdot 10^8 m/s[/tex]
So, the index of refraction is
[tex]n=\frac{3.00\cdot 10^8 m/s}{1.75\cdot 10^8 m/s}=1.71[/tex]
