Mirror 4-Momentum: Find Frequency Change on Reflection

In summary, a mirror with a speed of βc moves perpendicular to its plane while a light ray is incident on it from the "forward" direction with an incident angle θ. The angle of reflection, φ, can be found by calculating cos φ. The frequency of the light changes upon reflection by a factor that is not specified. In the rest frame of the mirror, the angle of reflection is equal to the angle of incidence and there is no frequency shift. The 4-momentum of the light after reflection can be found by consulting a teacher.
  • #1
SHawking01
13
0

Homework Statement


A mirror moves perpendicular to its plane with speed βc. A light ray is incident on the mirror from the “forward” direction (i.e., vm · vl < 0, where vm is the mirror’s 3-velocity and vl is the light ray’s 3-velocity) with incident angle θ (measured with respect to the mirror’s normal vector). (a) Find cos φ, where φ is the angle of reflection. (b) By what factor does the frequency of the light change upon reflection?

Homework Equations



None that I know of.

The Attempt at a Solution


P~ in = E c (sin θin , − cos θin , 0 , 1)
P~ ′ in = E c [γ(sin θin − β) , − cos θin , 0 , γ(1 − β sin θin)]
I don't know what else.
 
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  • #2
What happens in the mirror rest frame when the light is reflected?
 
  • #3
In the rest frame of the mirror the angle of reflection equals the angle of incidence and there is no frequency shift.
 
  • #4
So what will be the 4-momentum of the light after reflection?
 
  • #5
Well, I went to my teacher and found the answer. But thanks for your help anyways!
 

1. What is mirror 4-momentum?

Mirror 4-momentum is a concept in physics that describes the relationship between the frequency and wavelength of light before and after reflection off a mirror. It is a measure of how the momentum of light changes upon reflection.

2. How is mirror 4-momentum calculated?

Mirror 4-momentum can be calculated using the formula p = hf/c, where p is the 4-momentum, h is Planck's constant, f is the frequency of light, and c is the speed of light. This equation takes into account the change in frequency and the speed of light before and after reflection.

3. Why is mirror 4-momentum important?

Mirror 4-momentum is important because it helps us understand the behavior of light when it interacts with a reflective surface. It allows us to predict the change in frequency and wavelength of light upon reflection, which is essential in many applications such as designing optical instruments and studying the behavior of light in different mediums.

4. Can mirror 4-momentum be negative?

Yes, mirror 4-momentum can be negative. This occurs when the frequency of light decreases upon reflection, resulting in a negative change in momentum. This can happen when light reflects off a medium with a higher refractive index, such as glass.

5. How does mirror 4-momentum affect the color of an object?

Mirror 4-momentum does not directly affect the color of an object. However, it does determine the change in frequency and wavelength of light upon reflection, which can ultimately affect the perceived color of an object. For example, a red object may appear blue when viewed in a mirror due to the change in frequency of light upon reflection.

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