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

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Puneeth423
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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]
 
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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.