When light travels through the vacuum of space, it reaches its maximum possible speed. When this light enters any physical medium, such as ethyl alcohol, its speed is reduced. This article explains the physics behind this slowdown and determines the specific speed at which light travels when passing through ethyl alcohol.
Establishing the Universal Speed Limit
The speed of light in a perfect vacuum represents the absolute upper limit for velocity in the universe, a constant denoted by \(c\). This value is precisely defined as \(299,792,458\) meters per second, often approximated to \(3.00 \times 10^8\) meters per second. This maximum speed is a fundamental constant of nature and serves as the necessary baseline for all calculations. No particle with mass can reach this velocity, and all forms of electromagnetic radiation travel at this rate only when unimpeded by matter.
The Role of the Index of Refraction
Light slows down when it encounters a transparent medium because its photons interact with the electrons of the material’s atoms. The light energy is temporarily absorbed and then re-emitted by these electrons, causing a delay in the overall propagation of the light wave through the substance. Although the individual photons themselves are always moving at \(c\) between atoms, the net effect of this continuous interaction is a measurable decrease in the macroscopic speed of the light beam.
To quantify this phenomenon, physicists use the Index of Refraction, symbolized by \(n\). This dimensionless value is the mathematical ratio that expresses how much a given medium slows light down compared to a vacuum. The index of refraction is defined by the formula \(n = c/v\), where \(c\) is the speed of light in a vacuum and \(v\) is the speed of light in the specific medium.
Since the speed of light in any medium (\(v\)) is always less than \(c\), the index of refraction \(n\) for all materials is always greater than 1.0. For example, a substance with an index of refraction of 2 would slow the light down to half its vacuum speed.
Calculating the Speed in Ethyl Alcohol
Ethyl alcohol, also known as ethanol, is a common liquid whose optical properties have been well-measured. The standard index of refraction for pure ethyl alcohol is approximately \(n = 1.36\). This value is typically measured under specific conditions, such as standard temperature and pressure, and using light of a specific wavelength.
To determine the speed of light in ethyl alcohol, we rearrange the index of refraction formula to solve for the speed in the medium: \(v = c/n\). Substituting the known values, we perform the calculation: \(v = 299,792,458 \text{ m/s} / 1.36\).
The speed of light in ethyl alcohol is approximately \(220,435,630\) meters per second, or \(2.20 \times 10^8\) meters per second. This result confirms that light moves significantly slower through this liquid compared to a vacuum.
How Light’s Speed Affects Refraction
The change in light’s speed as it crosses the boundary between two different media leads directly to the observable phenomenon known as refraction. Refraction is the physical bending of a light ray at the interface between substances. This bending occurs because the part of the light wave that hits the new medium first slows down, while the rest of the wave continues at the original speed until it also enters the new material.
The difference between the speed of light in the air and its speed in ethyl alcohol dictates the extent of this bending. Air has an index of refraction very close to 1.0, meaning light travels through it at nearly \(c\). When the light ray hits the ethyl alcohol, it slows down to \(2.20 \times 10^8\) meters per second, causing it to change direction.
This effect is why an object, such as a spoon or a straw, appears visually “bent” or distorted when partially submerged in a glass of liquid. The light rays coming from the submerged portion of the object bend away from their original path as they exit the liquid and enter the air before reaching the observer’s eye.