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

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SUMMARY

The refractive index is defined as the ratio of the speed of light in a vacuum to the speed of light in a medium, expressed mathematically as refractive index = {speed of light in vacuum}/[speed of light in the medium]. This value is also equivalent to the ratio {sin i/sin r}, where i is the angle of incidence and r is the angle of refraction. The proof of this relationship is derived from Fermat's principle, which states that light travels along the path that requires the least time.

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  • Basic knowledge of trigonometric functions (sine)
  • Familiarity with the concept of refractive index
  • Knowledge of the speed of light in different media
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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.
 

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