How does light reflect off a moving angled mirror?

[h1a8]

Let c be the speed of light. I have a mirror in the north facing me but angled at 45 degrees north of east. I shoot a beam of light north towards it. But right before I send the beam the mirror has a velocity v towards the east. When the beam strikes the mirror does it reflect off at a right angle from the direction the beam was first shot (like it does when the mirror is not moving) or does it reflect off the mirror a different angle [like 90-arctan(c/v) degrees south of east]?

 

[K^2]

Both the angle and frequency will change, but I'm not feeling up to deriving the actual formula right now. Basically, the electric field in the outgoing wave must perfectly cancel the electric field in the incoming wave. If you consider a polarized, monochromatic, coherent plane wave, you should be able to derive the outgoing angle.

 

[h1a8]

Both the angle and frequency will change, but I'm not feeling up to deriving the actual formula right now. Basically, the electric field in the outgoing wave must perfectly cancel the electric field in the incoming wave. If you consider a polarized, monochromatic, coherent plane wave, you should be able to derive the outgoing angle.

Thanks! I was thinking more towards the topics of relative velocity and angle of incidence = angle of reflection. For example, if a beam moves north while a mirror, who begins perpendicular to the source (or facing it), moves east at velocity v then the velocity of the beam relative to the mirror would be (-v,c) making the angle of incidence arctan(c/|v|).
But if the mirror starting off tilted at 45 degrees north of east then the angle of incidence would be pi/4+arctan(c/|v|).

 

[K^2]

There are some fundamental problems with treating light as an "object" traveling at c. Sometimes it works out. Others, it gives you an error by some fixed factor, like the light beam being bent by gravity, the angle will be exactly 2 times off. Sometimes you get the exact opposite effect, like in refraction, where the light would bend the other way if it behaved like a particle.

There are also concerns with relativity. How does you approach account for relativistic Doppler shift when v->c?

Usually the best approach is to byte the bullet and work out what will happen to an electromagnetic wave.

 

[sardar]

The reflection of light off a moving angled mirror can be explained using the laws of reflection and the principle of relativity. According to the laws of reflection, the angle of incidence (the angle between the incoming light beam and the normal to the mirror surface) is equal to the angle of reflection (the angle between the reflected light beam and the normal to the mirror surface). This holds true regardless of the velocity of the mirror.

However, when the mirror is in motion, the angle of incidence and the angle of reflection are measured with respect to the mirror's frame of reference. This means that the observer standing in front of the mirror will measure the angle of incidence and the angle of reflection differently than an observer who is moving with the mirror. This is where the principle of relativity comes into play.

In your scenario, the observer standing in front of the mirror will see the light beam reflect off at a right angle from the direction it was first shot, as expected from the laws of reflection. However, the observer moving with the mirror will measure the angle of reflection to be slightly different. This is because the observer's frame of reference is also moving with the mirror, causing a shift in the angle of reflection.

To calculate the exact angle of reflection, we can use the equation 90-arctan(c/v) degrees, where c is the speed of light and v is the velocity of the mirror. This equation takes into account the relative motion between the observer and the mirror and gives a more accurate measurement of the angle of reflection.

In summary, the light will reflect off the moving angled mirror at a slightly different angle for an observer moving with the mirror, but for an observer standing in front of the mirror, it will still reflect at a right angle from the direction it was first shot. This phenomenon can be explained using the laws of reflection and the principle of relativity.