Velocity Vector of Light

In summary, an observer moving with a speed c.cos θ will see the light moving along y-axis with a speed c.sin θ that is different to the case where the observer is stationary and the light is moving along the propagation of light.
  • #1

bgq

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0
Hi,

Consider a source of light transmitting light at an angle θ with x-axis as seen in the following figure:

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Now an observer looking at x-axis will determine the speed of light to be c.cos θ, and the one looking at y-axis determine c.sin θ.

How can we resolve this according to the principle of constancy of speed of light.
 
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  • #2
bgq said:
How can we resolve this according to the principle of constancy of speed of light.
What's to resolve? The speed of light is constant (invariant), but any component depends on what axis you choose. (And furthermore, the direction of a given light pulse is also frame dependent.)
 
  • #3
Thanks Doc Al to your reply.

Consider an observer moving in the x direction with a speed c.cos θ.
According to this observer, there is no motion of the light along x-axis, so he will see the light moving parallel to y-axis with a speed c.sin θ ≠ c !
 
  • #4
bgq said:
Consider an observer moving in the x direction with a speed c.cos θ.
According to this observer, there is no motion of the light along x-axis, so he will see the light moving parallel to y-axis with a speed c.sin θ ≠ c !
No, it doesn't work that way. What he'll see is the light moving with speed c in the y-direction.

You might want to look up the relativistic velocity transformations. They will show that different observers will see the light traveling in different directions, but always with speed c.
 
  • #5
What confused me here is that time dilation and length contraction are not evident in the y direction because it is perpendicular to the motion. So the observer sees the light covers same distance during the same time along y-axis yielding v = c.sin (theta).

This is different to the case where the motion is along the propagation of light where time dilation and length contraction effects assure obtaining c for the speed of light.
 

1. What is the velocity vector of light?

The velocity vector of light refers to the direction and speed at which light travels through space. In a vacuum, light travels at a constant speed of approximately 299,792,458 meters per second (or about 186,282 miles per second).

2. How is the velocity vector of light measured?

The velocity vector of light can be measured using various methods, such as the Michelson-Morley experiment, which measures the speed of light by splitting a beam of light and recombining it using mirrors and measuring the interference pattern. It can also be measured using the frequency and wavelength of light, as they are directly related to its velocity.

3. What factors can affect the velocity vector of light?

The velocity vector of light can be affected by the medium through which it is traveling. In a vacuum, light travels at its maximum speed, but when passing through a medium such as water or air, it may slow down. The frequency and wavelength of light can also affect its velocity.

4. Why is the velocity vector of light important in science?

The velocity vector of light is important in science because it is a fundamental constant that is used in many equations and theories. It plays a crucial role in understanding the behavior of light and its interactions with matter, as well as in the study of relativity and the structure of the universe.

5. Can the velocity vector of light be exceeded?

According to the theory of relativity, the velocity of light is the maximum speed at which anything can travel. This means that it cannot be exceeded by any object or particle with mass. However, some theories suggest that the speed of light may not be constant in all situations, and there is ongoing research in this area.

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