What determines the direction visible light travels?

Question

What determines the direction visible light travels?

How do the energy state fluctuations of electrons relate to the direction of the visible light generated?

In which direction does an excited atom emit? (thank you Charles Tucker).

Answer 1

Your title is about visible light i.e. classical electromagnetic radiation, and the answer is that it follows classical optical rays starting from the source.

How do the energy state fluctuations of electrons relate to the direction of the visible light generated?

At the level of atoms and electrons we enter quantum mechanics, and in quantum electrodynamics light is a quantum superposition of a large number of photons. You can get an idea of how complex this superposition is from this double slit single photon at a time experiment, where the classical light interference appears as an accumulation of photons.

The light source here is a laser which creates a parallel beam of classical light, the way the individual photons emitted in the laser is seen here.

For usual light sources the coherence of phases is missing, and the classical light is a superposition of incoherent photons, depending on the exact geometry of the source.

In which direction does an excited atom emit?

As seen above in lasers the collective direction of light can be controlled by the phases of the photon wavefunctions. Generally, only the probability of photon creation in a given direction can be predicted in quantum mechanics, not an exact direction for a given transition.

Answer 2

What determines the direction visible light travels?

Light, by Fermat's principle of least time, travels the direction that gives the shortest time delay. In vacuum, or a homogeneous medium like air, that's a straight line. When heat makes the air nonhomogeneous, you will see images shimmer if viewed over a radiator, or observe mirages. And, by combining different materials, one can make an optical fiber or graded-index lens that guides light in curved paths.

Most simply, a prism bends light in such a way that the observed path is the peak-speed way for light to pass through air and glass so that no other path is speedier at connecting the light source with a designated point in the glass.
The speed in glass depends on the color of the light, so the minimum-time refraction angles are slightly different for different colors.

More complex, a few internal reflections in a sphere of water generates both transmission of light AND two internal reflections makes a local-minimum-delay path that we admire as a first-order rainbow. Other paths exist, one can occasionally see a second-order rainbow. The fact is, the global minimum of time delay (through the droplet with no reflections) is not the only local minimum of time delay solution, and some fraction of the incident light is showing us the alternate solution(s) to a minimum-delay path.

Yet more complex, a lens (which can be thought of as an array of different prisms) can form the images on our retinas that give us sight. For a thin lens, this can be shown to focus at a point all the light that originated at another point in space, by slowing the fastest (straight-line) path along the lens axis to equal the slower paths (bent paths with longer real in-air distance) that go through the off-axis parts of the lens. Thus, ALL those paths have the same (the minimum) delay, and all the light hits that focus spot.

And completely simply: if light didn't travel in straight lines in a vacuum, a curved path between any two points is longer than a straight line path, so takes more time. So, light doesn't follow any curved path when the straight line in fixed-speed light propogation is available.

How do the energy state fluctuations of electrons relate to the direction of the visible light generated?

Almost not at all. Energy is not directional, and most light sources (thermal ones) are very disordered, so emit light in all directions. There are exceptions, like cyclotron radiation, where a strong magnetic field creates polarized and directed light. To generate light with a direction, we usually use reflectors or shape the source to present more area facing in our favored direction (a disk shows more face to on-axis viewers than to those who see it edge-on).

In which direction does an excited atom emit?

There, the answer is complex. If the environment is filled with other radiation, the quickest (most likely) decay of an excited state occurs when a photon adds to an existing photon, rather than springing into existence spontaneously. That's called stimulated emission (the SE part of LASER). It doesn't even need to involve an excited atom, just an electron (in a synchrotron) will radiate preferentially in concert with any prevailing wave pattern, making a free-electron laser.