[Fussball (OP)]

Hi all. A 90 degree ray of light (from a star) hits a mirror (on the earth) that is slanted at 45 degrees. Then the ray goes to an eye piece.The angle made by the ray of light when it reaches the eye piece is 90 degrees. But as seen from the star frame, the 90 degree ray hits a contracted mirror (due to earth's motion and is no longer slanted at 45 degrees) and therefore the ray of light will miss the eye piece. What is the resolution to this problem?

[Kryptid]

Hi all. A 90 degree ray of light (from a star) hits a mirror (on the earth) that is slanted at 45 degrees. Then the ray goes to an eye piece.The angle made by the ray of light when it reaches the eye piece is 90 degrees. But as seen from the star frame, the 90 degree ray hits a contracted mirror (due to earth's motion and is no longer slanted at 45 degrees) and therefore the ray of light will miss the eye piece. What is the resolution to this problem?

This isn't something I've considered before. My best guess is that the space that the light beam travels through after it is reflected off the length-contracted mirror is also contracted, which distorts the trajectory of the beam such that it enters the eyepiece in all reference frames.

[Fussball (OP)]

On a moving mirror, according to relativistic law of reflection, the angle of reflection is not equal to the angle of incidence. Therefore, the angles can't be the same in both the frames. The star frame should see a different reflection than the earth frame. Meaning in one frame, the light misses the eye piece. Or the angle of reflection is the same in both the frames. But that contradicts relativistic law of reflection.

[Halc]

Hi all. A 90 degree ray of light (from a star) hits a mirror (on the earth) that is slanted at 45 degrees. Then the ray goes to an eye piece.The angle made by the ray of light when it reaches the eye piece is 90 degrees.

Angles require two lines/rays, and you're only describing one, so there's no angle at all except the angle formed at the mirror. So if I can guess the setup here, there's a light source on the left sending horizontal light towards a mirror oriented 45° wrt to this beam, deflecting the beam upward vertical to a sensor. If that's not the scenario, you need to post a correction.

But as seen from the star frame, the 90 degree ray hits a contracted mirror (due to earth's motion and is no longer slanted at 45 degrees)

It was nowhere stated, but if the mirror is contracted in the star frame, you're assuming the star is moving relative to the mirror.  The eyepiece is presumably stationary relative to the mirror else it would observer the ray coming from it only momentarily.

So give a receding star, in the star frame, the mirror and eyepiece are both receding and the reflection angle changes, and the light is deflected at say 100° sending each photon to the right of the point of reflection.  The eyepiece is also moving to the right and will intercept that beam perfectly, not miss it as you suggest.

[Halc]

On a moving mirror, according to relativistic law of reflection, the angle of reflection is not equal to the angle of incidence. Therefore, the angles can't be the same in both the frames. The star frame should see a different reflection than the earth frame. Meaning in one frame, the light misses the eye piece. Or the angle of reflection is the same in both the frames. But that contradicts relativistic law of reflection.

Let's say the mirror is moving really fast away.  The angle of incidence goes from 45° to closer to 0° as the contraction of the mirror forces it vertical.  The angle of reflection goes from 45° for a stationary mirror and approaches 180° (meaning it is barely deflected at all) and at some point between the angle of reflection is 90°, parallel to the mirror surface.  In no case does the eyepiece get missed.

The star does not see any reflection since the mirror is not vertical, so sends no light back to the star.

[Fussball (OP)]

If that's not the scenario, you need to post a correction.

I imagined star light coming from the top, hits a 45 degree mirror at the bottom, and the ray is then reflected to the right where there is an eye piece.

I think I see that the reflections occur as if there is no length contraction. Which means the ray does not miss the eye piece in either frame.

[Halc]

If that's not the scenario, you need to post a correction.

I imagined star light coming from the top, hits a 45 degree mirror at the bottom, and the ray is then reflected to the right where there is an eye piece.

Fine.  Just rotate my description a quarter turn clockwise and you have it. 

I think I see that the reflections occur as if there is no length contraction. Which means the ray does not miss the eye piece in either frame.

In the frame of the mirror, this is exactly what happens.  In other frames, the contraction changes the mirror angle to a lower angle of incidence, and changes the angle of reflection to nearly 180° for a receding mirror or 0° for an approaching mirror.  In no case does the eyepiece get missed, but the reflected beam is not perpendicular to the incoming ray.  It would miss the eyepiece (which is also moving) if it was reflected perpendicular like that.

[Fussball (OP)]

Does the paper mentioned in the link below verify relativistic law of reflection?

https://en.wikisource.org/wiki/Effect_of_Reflection_from_a_Moving_Mirror_on_the_Velocity_of_Light

"It appears therefore that within the limit of error of experiment (say 2 per cent) the velocity of a moving mirror is without influence on the velocity of light reflected from its surface."

[Halc]

Does the paper mentioned in the link below verify relativistic law of reflection?

https://en.wikisource.org/wiki/Effect_of_Reflection_from_a_Moving_Mirror_on_the_Velocity_of_Light

"It appears therefore that within the limit of error of experiment (say 2 per cent) the velocity of a moving mirror is without influence on the velocity of light reflected from its surface."

The experiment is not dated, but seems to be one setup to illustrate that the speed of light does not vary due to the speed of the mirror from which it reflects.  Since the mirror is always angled nearly perpendicular to the incident light beam, it isn't attempting to measure a different reflection angle, so no, the law of reflection is not referenced or tested by this setup.  A spinning mirror is lucky to get up much past the speed of sound let alone anywhere near enough speed to exhibit relativistic contraction.

The experiment in the paper was designed to distinguish between the emissions theory (or corpuscular) and undulatory (wave) theory of light.  Both theories were falsified eventually.

[Janus]

Does the paper mentioned in the link below verify relativistic law of reflection?

https://en.wikisource.org/wiki/Effect_of_Reflection_from_a_Moving_Mirror_on_the_Velocity_of_Light

"It appears therefore that within the limit of error of experiment (say 2 per cent) the velocity of a moving mirror is without influence on the velocity of light reflected from its surface."

In this particular experiment, the light path is perpendicular to the mirrors C and D, with the difference that mirror C is moving away from E upon reflection and Mirror D is moving towards E, In other words, the light in both cases is reflected back along its path. (I know that the illustration shows a small angle difference, but this is just so they don't have to draw the light paths on top of each other.)
Since in this case, the direction of the reflected light is not expected to change, it is fair to say that if the speed isn't effected, the velocity isn't.
However, if you are to use 45 degree tilted mirrors instead, the situation changes. The speed of the reflected light remains unchanged, but its direction and thus its velocity is effected.
There is an effect know as the aberration of light.  If you and I are moving relative to each other at some velocity along the X axis, and I fire a light beam along the Y axis,(90 degrees to our relative path as measured by me) then you will measure that same light as traveling at c but at an angle other than 90 degrees to the X axis.
So now imagine that I am standing next to a 45 degree angled mirror.  You fire a light beam at me. When the light strikes the mirror and reflects off at a 90 degree angle, I also fire my light at the same direction.   The two beams will be parallel.
You will measure my light as traveling at a non-ninety degree angle, and you will see the reflected beam travel along a parallel path.  You will not measure one as diverging from the other. 

[David Cooper]

Hi all. A 90 degree ray of light (from a star) hits a mirror (on the earth) that is slanted at 45 degrees. Then the ray goes to an eye piece.The angle made by the ray of light when it reaches the eye piece is 90 degrees. But as seen from the star frame, the 90 degree ray hits a contracted mirror (due to earth's motion and is no longer slanted at 45 degrees) and therefore the ray of light will miss the eye piece. What is the resolution to this problem?

You talk about 90 degrees for the angle of the light coming down from the star, and also 90 degrees for the angle it's moving at to the eyepiece, but what I think you mean is that it comes down vertically, reflects off the mirror, and then moves horizontally to the eyepiece. What you need to do to understand this is turn your light from a vertical line into a series of short horizontal lines to represent wave fronts. If you watch one of those wave fronts meeting the mirror, you'll notice that different parts of the lines touch at different times. That's of no importance when the mirror is stationary, but if the Earth and star are moving sideways at high speed, the effective angle of the mirror is very different from its actual angle. You should move the wave front down in a series of jumps and move the mirror along to the side in a series of jumps too, drawing a mark on the background in line with where the line of the wave front and the line of the mirror intersect. You can then draw a line through all your dots on the background to get a new line which is the effective angle of the mirror. That effective angle is the one that tells you how the light actually reflects off the mirror. To complete the job, of course, you have to apply the correct contraction to the mirror when it's moving, and you also have to use the actual angle that the light is following to get from the star to the Earth which will not be a vertical line. When you do this properly you will find that the light leaves the mirror horizontally and goes to the eyepiece. To give you some examples of angles, if the star and Earth are moving to the right at 86.6% the speed of light, the light that you think is coming down vertically from the star is actually following a path 60 degrees away from that direction, and the mirror is contracted to make its actual angle something around 63.4 degrees to the horizontal rather than 45 that someone travelling with the Earth sees it as. When you draw the dots on the background to get the effective angle of the mirror, it will either be 75 or 15 degrees to the horizontal (depending on whether you're bouncing the light to the left or the right, and in both cases that will send the light which is coming down at 30 degrees to the horizontal onto a horizontal path to the eyepiece.

[Fussball (OP)]

However, if you are to use 45 degree tilted mirrors instead, the situation changes. The speed of the reflected light remains unchanged, but its direction and thus its velocity is effected.

Yes indeed. But the mirrors would have to spin at a very high rate to verify relativistic reflection.

[Fussball (OP)]

That's of no importance when the mirror is stationary, but if the Earth and star are moving sideways at high speed, the effective angle of the mirror is very different from its actual angle. You should move the wave front down in a series of jumps and move the mirror along to the side in a series of jumps too, drawing a mark on the background in line with where the line of the wave front and the line of the mirror intersect. You can then draw a line through all your dots on the background to get a new line which is the effective angle of the mirror.

I see what you mean.

[Fussball (OP)]

There is an effect know as the aberration of light.

Best way to measure relativistic aberration (beaming) is to use light emitting particles that are moving at speeds very close to light. Light emitted by these particles will slant in the direction of the motion of the particles. Meaning the particles will be visible in only one direction. Change the angle of view you will not see the particles. Not sure an experiment like this has been performed.

[Fussball (OP)]

Does relativistic law of reflection apply to a light clock? Is the angle of incidence not equal to the angle of reflection? I wrote to a journal about this, they got back saying, relativistic law of reflection does not apply to horizontal mirrors. I thought they were just making stuff up.

[Halc]

Does relativistic law of reflection apply to a light clock? Is the angle of incidence not equal to the angle of reflection? I wrote to a journal about this, they got back saying, relativistic law of reflection does not apply to horizontal mirrors. I thought they were just making stuff up.

It doesn't apply to horizontal or vertical mirrors, but if you hold the light clock at some angle between, it very much applies.

[Janus]

There is an effect know as the aberration of light.

Best way to measure relativistic aberration (beaming) is to use light emitting particles that are moving at speeds very close to light. Light emitted by these particles will slant in the direction of the motion of the particles. Meaning the particles will be visible in only one direction. Change the angle of view you will not see the particles. Not sure an experiment like this has been performed.

We know that aberration is real, as we see with stellar aberration ( the apparent shift in the position of stars caused by the Earth's orbital motion.)

[CPT ArkAngel]

The eyepiece is at rest relative to the mirror. Everything at rest relative to the mirror has the same space-time distortion relative to the star... Neglecting any gravitational effect on space-time.

[Fussball (OP)]

It doesn't apply to horizontal or vertical mirrors,

Why do you think that is?

[Fussball (OP)]

We know that aberration is real, as we see with stellar aberration ( the apparent shift in the position of stars caused by the Earth's orbital motion.)

Relativistic aberration (or beaming) is different than classical or stellar aberration.