Inside glass, can I apply relativity of speed for light?

[LCSphysicist]

Homework Statement

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Relevant Equations

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I was doing a exercise which considerst he time it takes for light travels a glass with thickness proper D and velocity v. The speed of light is c/n inside the glass.

Now, my approach was to go to the glass frame, take the relative speed between the glass and the light using the trivial formula for addition of velocity in SR, so i would got $r$. The time it would take is $D/r$ and the distance $D$. SO i would apply Lorentz transformations to go back to the ground frame.

But the answer was simply $D/(c/n)$. Now we can understand what does this answer apply: speed of light is the same in all frame.

But, i though that the right way to interpret special relativity was that the maximum and "unique(in all frame)" speed is c, coincidentally this is the speed of light in vacuum.
And not that maximum and "unique(in all frame)" speed is the speed of light, which in vacuum is c.

I think you can see the difference and how this implies different answer to the question.

So, my interpretation is wrong? Or both are equivalent? what am i missing?

 

[PeroK]

Homework Statement:: .
Relevant Equations:: .

I was doing a exercise which considerst he time it takes for light travels a glass with thickness proper D and velocity v. The speed of light is c/n inside the glass.

Now, my approach was to go to the glass frame, take the relative speed between the glass and the light using the trivial formula for addition of velocity in SR, so i would got $r$. The time it would take is $D/r$ and the distance $D$. SO i would apply Lorentz transformations to go back to the ground frame.

But the answer was simply $D/(c/n)$. Now we can understand what does this answer apply: speed of light is the same in all frame.

But, i though that the right way to interpret special relativity was that the maximum and "unique(in all frame)" speed is c, coincidentally this is the speed of light in vacuum.
And not that maximum and "unique(in all frame)" speed is the speed of light, which in vacuum is c.

I think you can see the difference and how this implies different answer to the question.

So, my interpretation is wrong? Or both are equivalent? what am i missing?

I'm not sure I totally understand your question, but the following applies:

Velocity addition uses the universal invariant speed $c$.

This speed is (somewhat coincidentally) also the speed of light in vacuum.

The speed of light in a medium is not $c$ and so there is nothing special about this speed. In other words, $c/n$ is just another subluminal speed with nothing special in terms of velocity addition or relativistic kinematics.

 

[Orodruin]

What is your $r$?

$Dn/c$ is wrong. It is the time taken in the glass rest frame.

 

[LCSphysicist]

The speed of light in a medium is not $c$ and so there is nothing special about this speed. In other words, $c/n$ is just another subluminal speed with nothing special in terms of velocity addition or relativistic kinematics.

That was my point. So we agree with that.

What is your $r$?

$Dn/c$ is wrong. It is the time taken in the glass rest frame.

r would be, $r = (c/n - v)/(1-v/cn)$
So here i can't understand, the time in glass rest frame shouldn't be $D/r = \frac{D}{(c/n - v)/(1-v/cn)}$? $Dn/c$ does not assume that "c/n" is the same in any frame?

 

[PeroK]

So here i can't understand, the time in glass rest frame shouldn't be $D/r = \frac{D}{(c/n - v)/(1-v/cn)}$? $Dn/c$ does not assume that "c/n" is the same in any frame?

The time in the glass frame must be $\frac D{c/n}$. That's simply what it means for the speed of light in glass to be $c/n$.

You can transform to a frame in which the glass moves at $v$ by the usual approach: length contraction and velocity addition, for example. Or, use the Lorentz transformation.