Why Is the Denominator in Fermat's Principle (c/n) Instead of (cn)?

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SUMMARY

The denominator in Fermat's Principle is correctly represented as (c/n) rather than (cn) because it reflects the time taken for light to traverse a distance ds in a medium. The speed of light in a medium is always less than c, and the refractive index (n) is defined to be greater than one, ensuring that (c/n) yields a sensible result. This formulation confirms that light takes longer to travel through a medium compared to a vacuum, adhering to the principles of optics.

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manimaran1605
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The expression gives time taken to reach a a distance ds in a medium.
The expression has the dimension of time, But my question is how come the denominator is (c/n)? why it can't be (cn)? explain me.
 

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Bearing in mind that the speed through a medium must always be less than c and that refractive index is always specified such that it is greater than unity. Using c/n produces the sensible answer, which is that light will always take longer to travel through a medium than through a vacuum.
IF n were defined the other way round, then your alternative would apply.
 

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