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

In summary: But, I think it's clear from what you've written that you're not asking about how to do these things in a specific frame, you're asking about the answer to a question about the speed of light in general.
  • #1
LCSphysicist
646
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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?
 
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  • #2
Herculi said:
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.
 
  • #3
What is your ##r##?

##Dn/c## is wrong. It is the time taken in the glass rest frame.
 
  • #4
PeroK said:
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.
Orodruin said:
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?
 
  • #5
Herculi said:
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.
 

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

1. Can light travel at different speeds inside glass?

Yes, light can travel at different speeds inside glass due to the phenomenon of refraction. The speed of light in a vacuum is approximately 299,792,458 meters per second, but when it enters a medium like glass, its speed decreases. This is because light interacts with the atoms and molecules in the glass, causing it to slow down.

2. How does the speed of light inside glass compare to its speed in a vacuum?

The speed of light inside glass is slower than its speed in a vacuum. The exact speed depends on the type of glass and its composition, but it is typically around 200,000,000 meters per second. This is still incredibly fast, but it is significantly slower than its speed in a vacuum.

3. Does the theory of relativity apply to the speed of light inside glass?

Yes, the theory of relativity still applies to the speed of light inside glass. According to the theory, the speed of light is constant in all reference frames, regardless of the medium it is traveling through. This means that even though the speed of light is slower in glass, it is still the same for all observers, regardless of their relative motion.

4. Can the speed of light inside glass be changed?

Yes, the speed of light inside glass can be changed by altering the properties of the glass. For example, different types of glass have different refractive indexes, which affects the speed of light. Additionally, the temperature and pressure of the glass can also impact the speed of light. However, the speed of light inside glass can never exceed the speed of light in a vacuum.

5. How does the speed of light inside glass affect our perception of objects?

The speed of light inside glass can affect our perception of objects by causing them to appear distorted or shifted. This is because the light rays that reach our eyes are bent as they travel through the glass, resulting in a different image than what we would see without the glass. This is why objects may appear larger or smaller when viewed through a magnifying glass, which is made of glass with a curved shape that causes the light to bend in a specific way.

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