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

[manimaran1605]

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.

 

[sophiecentaur]

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.