Can Snell's Law Be Proven Mathematically for Sound and Light Refraction?

[Misr]

when light rays fall perpendicularly on a separating surface between two media it doesn't refract according to Snell's law
and it is the same with sound waves

how to prove something like that mathematically??
Thanks in advance

 

[JeffKoch]

when light rays fall perpendicularly on a separating surface between two media it doesn't refract according to Snell's law
and it is the same with sound waves

how to prove something like that mathematically??
Thanks in advance

You mean using something other than Snell's law, which mathematically says that there is no refraction?

 

[Misr]

No I mean using Snell's Law

which mathematically says that there is no refraction?

I want to know how

 

[Lobezno]

Well the sin 90 degrees, or perpendicularity, is 1. So...multiplying any number by zero will give the same number, ergo no refraction.

 

[Misr]

Well the sin 90 degrees, or perpendicularity, is 1. So...multiplying any number by zero will give the same number, ergo no refraction.

I don't understand what are you trying to say but when light falls perpendicular to the surface means that the angle is 0 not 90
so on appling snells law
n1sin(θ1) = n2sin(θ2)
where sin0=0
therefore n2sin(θ2)=0
and since n2 can't be zero of course
then θ2=0 so no refraction takes place
right?

 

[JeffKoch]

I don't understand what are you trying to say but when light falls perpendicular to the surface means that the angle is 0 not 90
so on appling snells law
n1sin(θ1) = n2sin(θ2)
where sin0=0
therefore n2sin(θ2)=0
and since n2 can't be zero of course
then θ2=0 so no refraction takes place
right?

Yes. "No refraction" means the two angles are the same, and 0=0, ergo there is no refraction.

 

[Misr]

Oh ok thanks very much

 

[Claude Bile]

More fundamentally, the wave-vector component parallel to the interface must be constant across the interface to ensure continuity between EM fields in both media. Snell's law is derived from this condition.

When a wave strikes a boundary at normal incidence, there is no wave-vector component parallel to the interface (by definition). Due to continuity, there can be no parallel wave-vector component in either medium, and so the wave is not deflected in any way.

This is what Snells law says in a nutshell.

Claude.