Speed of light Knowledge-Based Study

Study notes

1. What is the Speed of Light?

   Light is an electromagnetic wave that propagates through space by transferring energy via oscillating electric and magnetic fields. In a vacuum, light travels at a fundamental physical constant denoted by the symbol $c$.

   The exact value of the speed of light in a vacuum is defined as:

   $$c = 299{,}792{,}458\text{ m/s}$$

   For most practical calculations in physics, this value is rounded to three significant figures:

   $$c \approx 3.00 \times 10^8\text{ m/s}$$

   According to the principles of modern physics, $c$ is the universal speed limit; no mass or information can travel faster through space than the speed of light in a vacuum.

   How Mediums Affect Light Speed

   When light passes from a vacuum into a transparent material medium—such as air, water, or glass—its speed decreases. This slowing occurs because the electromagnetic fields of the light interact with the charged particles inside the material.

   The speed of light inside a specific medium ($v$) is governed by the medium's index of refraction ($n$):

   $$n = \frac{c}{v}$$

   • Vacuum: $n = 1.00$ exactly, so $v = c$.
   • Air: $n \approx 1.0003$, so light slows down only negligibly.
   • Water: $n \approx 1.33$, resulting in $v \approx 2.26 \times 10^8\text{ m/s}$.
   • Crown Glass: $n \approx 1.52$, resulting in $v \approx 1.97 \times 10^8\text{ m/s}$.
   • Diamond: $n \approx 2.42$, resulting in $v \approx 1.24 \times 10^8\text{ m/s}$.

   Because the speed in any material is strictly less than $c$, the index of refraction of any physical substance is always greater than or equal to 1 ($n \ge 1$).

   Wavelength, Frequency, and Bending

   The wave nature of light relates its propagation speed ($v$), frequency ($f$), and wavelength ($\lambda$) through the wave equation:

   $$v = f\lambda$$

   When a light wave crosses an interface between two different media:

   • Frequency ($f$): Remains unchanged because it is determined solely by the source generating the wave.
   • Speed ($v$): Changes based on the index of refraction of the new medium.
   • Wavelength ($\lambda$): Adjusts proportionally to the change in speed ($\lambda = \frac{\lambda_0}{n}$, where $\lambda_0$ is the wavelength in a vacuum).

   This difference in speed between two media is the underlying physical cause of refraction—the bending of light rays as they transition from one medium into another.