Final answer:
The speed of light in a vacuum is constant and does not change due to gravity or motion. In mediums, light's speed decreases and varies with wavelength, returning to the constant speed when re-entering a vacuum. Gravity affects the path of light but not its intrinsic speed.
Step-by-step explanation:
The question of whether the speed of light increases when falling is rooted in the understanding of special and general relativity in physics. In a vacuum, the speed of light is a constant (c) and does not change regardless of the light's source or the observer's frame of reference. According to Einstein's general relativity, gravity can bend the path of light, just as it bends the trajectories of physical objects. This is analogous to light propagating through an upward-accelerating elevator, where it strikes a different point than if the elevator were stationary due to the relative motion of the elevator and the speed of light being constant.
In mediums such as air or glass, light behaves differently. As light enters a denser medium like glass, its speed decreases, and the ray bends towards the normal line, known as refraction. This results in different wavelengths of light traveling at different speeds inside the medium. Violet light with a shorter wavelength slows down more than orange light with a longer wavelength. However, when the light exits the medium and re-enters a vacuum, its speed returns to c, since its speed is not dependent on forces acting upon it like friction in mechanical situations. When a beam of light passes near a massive object like the Sun, the strong gravitational field can affect the passage of time and space itself. This can result in a delay in arrival time for light or radio waves, which is observable and measurable. Nevertheless, this does not equate to a change in the intrinsic speed of light; rather, it indicates that the path the light takes through curved spacetime is elongated, leading to an increased travel time.