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

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The denominator in Fermat's Principle is (c/n) because it accurately represents the time taken for light to travel a distance ds in a medium, where n is the refractive index. This formulation ensures that the speed of light in a medium is always less than the speed of light in a vacuum (c). Using (cn) would yield incorrect results, as it would imply that light travels faster in a medium than in a vacuum. The refractive index is defined as greater than unity, reinforcing that light takes longer to traverse a medium compared to a vacuum. Therefore, (c/n) is the correct expression for this principle.
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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