The relationship between the speed of light in a medium and the index of refraction is given by the formula:
\[ n = \frac{c}{v} \]
where:
- \( n \) is the index of refraction,
- \( c \) is the speed of light in a vacuum (approximately \( 300,000,000 \) m/s),
- \( v \) is the speed of light in the medium.
From this equation, we can see that as the speed of light (\( v \)) decreases in a medium, the index of refraction (\( n \)) increases. Therefore, the index of refraction is inversely proportional to the speed of light in the medium.
So the correct response is:
C. The index is inversely proportional to the speed of light in the medium.