Speed of light in a moving medium

[jobyts]

Let's say the speed of light in a medium is c'. Assume that the medium itself is moving at a very high speed v (close to c). What is the speed of light in the moving medium if
a. light and medium are moving in the same direction.
b. opposite direction (can the speed be zero or negative?)
c. in perpendicular.

 

[sylas]

Assuming an isotropic medium, the speed of light in the medium is less than c. The question states that it is c'.

If the medium is moving in same direction as the light, from the perspective of some external observer, then the corresponding speed of the light for that observer is given by the SR forumla for adding velocities.

$$\frac{v+c'}{1+vc'/c^2}$$​

I think that the transverse velocity of the medium is irrelevant, but I am checking that to see if my hunch is correct.

If v is greater than c' and in the opposite direction, then indeed the light in the isotropic refractive medium is moving backwards, respective to the external observer.

Cheers -- sylas

 

[astrokreng]

I would like to clarify that the speed of light in a vacuum, denoted as "c", is a fundamental constant and is the maximum speed at which all particles and information in the universe can travel. However, the speed of light in a medium, denoted as "c'", can be different from c due to the interaction of light with the particles in the medium. This phenomenon is known as the "refractive index" of the medium.

Now, let's address the given scenario of the speed of light in a moving medium. If the medium itself is moving at a very high speed v (close to c), the speed of light in the moving medium, denoted as "c'v", will be slightly different from the speed of light in a stationary medium. The exact value of c'v will depend on the refractive index of the medium and the direction of motion of the light and the medium.

In the case of light and medium moving in the same direction, the speed of light in the moving medium will be slightly less than c' due to the added velocity of the medium. This can be calculated using the Galilean transformation, which states that the velocity of light in a moving medium is equal to the velocity of light in a stationary medium minus the velocity of the medium. Therefore, in this scenario, the speed of light in the moving medium will be c'v = c' - v.

In the case of light and medium moving in opposite directions, the speed of light in the moving medium can approach zero, but it cannot be negative. This is because the speed of light in a medium cannot be negative, and the relative velocity between the light and the medium cannot exceed the speed of light in a vacuum. Therefore, in this scenario, the speed of light in the moving medium will be c'v = c' + v, but it cannot be less than zero.

In the case of light and medium moving in perpendicular directions, the speed of light in the moving medium will be slightly less than c' due to the added velocity of the medium in one direction. However, the exact value of c'v will depend on the angle between the direction of light and the direction of motion of the medium. In this scenario, the speed of light in the moving medium can be calculated using the vector addition of velocities.

In conclusion, the speed of light in a moving medium can vary depending on the direction of motion of the