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

In summary, the expression for the time taken to reach a distance ds in a medium has the dimension of time. The denominator is (c/n) because the speed through a medium must always be less than c and the refractive index is always greater than unity. This results in a sensible answer, where light will always take longer to travel through a medium than through a vacuum. If n were defined in the opposite way, then (cn) would be the correct denominator.
  • #1
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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  • #2
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.
 

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

What is Fermat's Principle expression?

Fermat's Principle expression is a fundamental law in optics that states that light will take the path of least time when traveling between two points.

Who developed Fermat's Principle expression?

Fermat's Principle expression was developed by French mathematician and physicist Pierre de Fermat in the 17th century.

How does Fermat's Principle expression relate to the behavior of light?

Fermat's Principle expression explains the behavior of light by stating that light travels in the path that will take the least amount of time, rather than the shortest distance.

What are the applications of Fermat's Principle expression?

Fermat's Principle expression has applications in various fields such as optics, mechanics, and electromagnetism. It is used to predict the path of light in different mediums and to calculate the refraction of light at boundaries between different materials.

Is Fermat's Principle expression always accurate?

While Fermat's Principle expression is a useful tool for predicting the behavior of light, it is not always accurate. In certain situations, such as when light travels through a medium with varying refractive indices, the principle may not hold true.

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