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

AI Thread Summary
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
Messages
60
Reaction score
0
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.
 

Attachments

  • time taken.PNG
    time taken.PNG
    10 KB · Views: 515
Physics news on Phys.org
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.
 

Thread 'The Physics of unloading sand from a barge'

I think it's easist first to watch a short vidio clip I find these videos very relaxing to watch .. I got to thinking is this being done in the most efficient way? The sand has to be suspended in the water to move it to the outlet ... The faster the water , the more turbulance and the sand stays suspended, so it seems to me the rule of thumb is the hose be aimed towards the outlet at all times .. Many times the workers hit the sand directly which will greatly reduce the water...
View full post »

Similar threads

I Is Fermat’s principle appicable to a plane wave?
Replies
12
Views
2K
How does Fermat's Principle follow from Huygen's principle?
Replies
1
Views
3K
A Why does the principle of stationary action work?
Replies
3
Views
2K
I Fermat's principle of least time
Replies
4
Views
2K
Does Fermat's Principle Apply in All Special Cases of Light Path Alteration?
Replies
38
Views
6K
I Does Light Travel the Shortest Path in Curved Space-Time Around a Neutron Star?
2
Replies
82
Views
4K
A Inertial mass, the Higgs field, and Mach's Principle
Replies
3
Views
131
Fermat & Snell: Solving the Derivation Mystery
Replies
2
Views
2K
B Fermat's Last Theorem; unacceptable proof, why?
Replies
12
Views
3K
I Is "nondimensionalization" a misnomer?
Replies
19
Views
2K

Hot Threads

Recent Insights

Back
Top