Proof That {sin i/sin r} = Refractive Index

[Puneeth423]

Refractive index = {speed of light in vacuum}/[speed of light in the medium]
This value also equals the ratio{sin i/ sin r}
Is there any mathematical proof showing that
{sin i/ sin r}= {speed of light in vacuum}/[speed of light in the medium]

 

[1994Bhaskar]

The relationship between refractive index and speed of light is by it's definition.The result sin i/ sin r is obtained by Fermat's principle which says light travels a path in shortest time.