Relativistic Doppler effect and refraction

[ahmadphy]

When an observer is inside a transparent medium moving relative to a light source located outside the medium, and the light enters the medium at an angle of incidence, how would relativistic effects—such as the frequency shift of the light observed due to relative motion—impact the angle of refraction as perceived by the moving observer? Specifically, would this angle differ from that perceived by a stationary observer within the same medium

 

[jbriggs444]

When an observer is inside a transparent medium moving relative to a light source located outside the medium, and the light enters the medium at an angle of incidence, how would relativistic effects—such as the frequency shift of the light observed due to relative motion—impact the angle of refraction as perceived by the moving observer? Specifically, would this angle differ from that perceived by a stationary observer within the same medium

You know about relativistic aberration?

Once you account for the aberration in the incident angle of light as measured in the observer's frame (the rest frame of the refractive medium) and any frequency correction due to Doppler, refraction is perfectly ordinary.

Naturally, a "stationary" observer will observe that the angle of incidence and the angle of refraction will be different due to aberration. However, as for frequency shift, a "stationary" observer would hardly expect that the frequency of light that he measures will be relevant for any frequency-sensitive refractive index in the moving medium.

 

[ahmadphy]

You know about relativistic aberration?

Once you account for the aberration in the incident angle of light as measured in the observer's frame (the rest frame of the refractive medium) and any frequency correction due to Doppler, refraction is perfectly ordinary.

Naturally, a "stationary" observer will observe that the angle of incidence and the angle of refraction will be different due to aberration. However, as for frequency shift, a "stationary" observer would hardly expect that the frequency of light that he measures will be relevant for any frequency-sensitive refractive index in the moving medium.

Thanks.
No I didn't know about relativistic abberation but now I do

 

[ahmadphy]

You know about relativistic aberration?

Once you account for the aberration in the incident angle of light as measured in the observer's frame (the rest frame of the refractive medium) and any frequency correction due to Doppler, refraction is perfectly ordinary.

Naturally, a "stationary" observer will observe that the angle of incidence and the angle of refraction will be different due to aberration. However, as for frequency shift, a "stationary" observer would hardly expect that the frequency of light that he measures will be relevant for any frequency-sensitive refractive index in the moving medium.

One more thing
When the light enters the medium, its velocity decreases to c/n . As a result, the Doppler shift changes, affecting the wavelength and consequently the refractive index. Does this imply that the light will follow a curved path?

 

[Orodruin]

What makes you think the index of refraction would change?

 

[ahmadphy]

What makes you think the index of refraction would change?

Because it depends on the wavelength which will change due to Doppler effect

 

[Orodruin]

Because it depends on the wavelength which will change due to Doppler effect

No. That’s not how things work. The refractive index is relevant only in the rest frame of the medium. If you want to know about any other frame you need to transfer the results from the rest frame to a frame where the medium moves.

You may want to check out Fizeau’s experiment.

 

[ahmadphy]

No. That’s not how things work. The refractive index is relevant only in the rest frame of the medium. If you want to know about any other frame you need to transfer the results from the rest frame to a frame where the medium moves.

You may want to check out Fizeau’s experiment.

You make a great point that the refractive index is formally defined in the rest frame of the medium, and transforming results to a moving frame is necessary for consistency. However, I'd like to delve deeper into the idea of a frame-dependent refractive index. Since the observed frequency or wavelength in a moving frame differs due to relativistic Doppler effects, wouldn't the material's dispersion relationship—being frequency-dependent—lead to an effective refractive index in that frame?

While the medium's properties are indeed frame-specific, the way light interacts with the medium from the perspective of a moving observer seems like it could be reframed. Could this approach be a valid way to interpret the refraction angle relative to the moving frame?

 

[jbriggs444]

While the medium's properties are indeed frame-specific, the way light interacts with the medium from the perspective of a moving observer seems like it could be reframed. Could this approach be a valid way to interpret the refraction angle relative to the moving frame?

Consider a light pulse incident on a moving surface. Would you expect that the angle of refraction "upstream" would differ from the angle of refraction "downstream"?

If so, then the classical law of refraction given by Snell's law: $\frac{\sin \theta_\text{incidence}}{\sin \theta_\text{refraction}} = n$ cannot hold. So a frame-dependent index of refraction is of questionable utility.

 

[ahmadphy]

Consider a light pulse incident on a moving surface. Would you expect that the angle of refraction "upstream" would differ from the angle of refraction "downstream"?

If so, then the classical law of refraction given by Snell's law: $\frac{\sin \theta_\text{incidence}}{\sin \theta_\text{refraction}} = n$ cannot hold. So a frame-dependent index of refraction is of questionable utility.

Your mention of upstream and downstream introduces a fascinating consideration However when incorporating relativistic effects one must account for the frame-dependence of key quantities such as the frequency of light and the refractive index As these quantities shift based on the observer's frame the behavior of light at the boundary can appear altered.

In this context Snell's law, which governs the relationship between the angles of incidence and refraction assumes a consistent refractive index. Yet, under relativistic conditions—where the refractive index becomes frame-dependent due to the Doppler-shifted frequency—Snell's law as traditionally formulated may no longer hold Instead it would require modification to account for relativistic transformations leading to potential violations in the classical sense.

Additionally just as in Compton scattering where frequency shifts emerge from the relative motion of the electron the Doppler-like shifts in this situation might similarly impact the angles of refraction upstream versus downstream This could make the angles frame-dependent and result in what appears as a deviation from Snell's law

 

[Orodruin]

Since the observed frequency or wavelength in a moving frame differs due to relativistic Doppler effects, wouldn't the material's dispersion relationship—being frequency-dependent—lead to an effective refractive index in that frame?

No. It would be direction dependent. In fact, it would not be in the typical easy form you are used to but likely be in the form of a rank 2 tensor. Trying to represent it with a frame dependent scalar would just fail.