Question

Light travels 875 km in material “x” in 5.00 ms. Calculate the speed of light in the material and the material’s index of refraction
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Answer 1

1. Speed of light in the material: $1.75\cdot 10^8 m/s$

The speed of light in a material is defined as follows:

$v=\frac{d}{t}$

where

d is the distance travelled by light in the material

t is the time taken

In this problem, we have

$d=875 km = 8.75\cdot 10^5 m$ is the distance travelled in the material

$t=5.00 ms=0.005 s$ is the time taken

So, the speed of light in the material is

$v=\frac{8.75\cdot 10^5 m}{0.005 s}=1.75\cdot 10^8 m/s$

2. Index of refraction: 1.71

The index of refraction of a material is defined as:

$n=\frac{c}{v}$

where

$c=3.00\cdot 10^8 m/s$ is the speed of light in a vacuum

v is the speed of light in the material

For this material, we have

$v=1.75\cdot 10^8 m/s$

So, the index of refraction is

$n=\frac{3.00\cdot 10^8 m/s}{1.75\cdot 10^8 m/s}=1.71$