What is meant by the frequency of light? How is frequency related to wavelength?

Wavelength is a fundamental attribute of waves, including ripples on a pond, sound in air, and particularly light waves. For light and all electromagnetic radiation, it's defined as the distance between successive peaks or troughs of a wave. Imagine watching ocean waves roll in; wavelength is the distance from the crest of one wave to the crest of the next. It’s measured in various units depending on the context, but for light, it's typically expressed in meters (m), nanometers (nm), or Angstroms (Å), with 1 m being equal to 10⁹ nm or 10¹⁰ Å.

In terms of practical applications, wavelength is directly tied to the color of visible light; each color we see corresponds to a different wavelength. Violet has the shortest wavelengths that humans can see, followed by the other colors of the rainbow up to red, which has the longest visible wavelengths.

The speed of light is a crucial constant in physics, symbolized as 'c'. Its value is approximately 299,792,458 meters per second (m/s) in a vacuum, which can be rounded to 3.00 x 10⁸ m/s for ease of calculations. This speed is the ultimate speed limit of the universe, meaning no matter or information can travel faster than light in a vacuum.

What makes the speed of light so important is its role in the fundamental laws of the universe. It is the key component in Einstein's famous equation, E=mc², linking energy (E) to mass (m). Furthermore, the consistent speed of light despite the observer's speed is the basis for the theory of relativity, which has a profound impact on how we understand space and time.

Hertz (Hz) is the unit of frequency named after the German physicist Heinrich Hertz. One Hertz corresponds to one cycle per second. It's a measure of how often a repeating event such as a wave cycle happens in the span of a second.

In the context of light, when we say that a light source has a frequency of 500 terahertz (THz), we are saying that its electromagnetic waves are oscillating 500 trillion times every second. This frequency determines the light's color: red light has a lower frequency and, consequently, lower energy; blue light has a higher frequency with higher energy. When discussing radio waves, frequencies are much lower, often in the kilohertz (kHz) to gigahertz (GHz) range. This characteristic allows us to categorize different forms of electromagnetic radiation across the spectrum, from radio waves to gamma rays.

A wave cycle in the context of light refers to one complete wave pattern, starting at any point on a wave and ending when the wave reaches the same point again after one complete oscillation. It encompasses a crest (the highest point of the wave) and a trough (the lowest point of the wave). The number of these cycles that happen in a second is what we call the frequency.

Understanding wave cycles is key to not just comprehending light, but all types of waves, including sound and even the probability waves described in quantum mechanics. Wave cycles illustrate the repetitive and periodic nature of waves, which is essential when it comes to analyzing and manipulating waves for various applications such as communications, medicine, and imaging technologies.