The order of the colors in the visible spectrum can be remembered by the acronym ROY G. BIV, which stands for red, orange, yellow, green, blue, indigo, violet. In the acronym, are the colors arranged in order of increasing or decreasing wavelength? In order of increasing or decreasing energy?

The relationship between wavelength and frequency is a fundamental concept in understanding the nature of light. A wavelength, represented by the Greek letter lambda \textbf{(\(λ\))}, measures the distance between corresponding points in a wave cycle, such as peak to peak or trough to trough. Frequency, denoted by the Greek letter nu \textbf{(\(ν\))}, refers to the number of wave cycles that pass a given point per second.

A handy way to imagine this is to think of waves on a beach: long, slow waves have a long wavelength and low frequency, whereas short, quick waves have a short wavelength and high frequency. These two properties are inversely related; as the wavelength increases, the frequency decreases and vice versa. This inverse relationship can be described by the equation \textbf{\(c = λν\)}, where \textbf{\(c\)} represents the speed of light in a vacuum, approximately \textbf{3 x 10^8 meters per second}.

Why is this important? Because this relationship helps determine how light of different colors behaves. For example, red light waves are longer and therefore have a lower frequency compared to blue or violet light waves.

Photon energy is a measure of the energy carried by a single particle of light, known as a photon. The energy of a photon is directly proportional to its frequency—and because of the inverse relationship with wavelength, it also means photon energy is inversely proportional to wavelength.

The equation \textbf{\(E = hν\)} encapsulates this relationship, where \textbf{\(E\)} is the energy of the photon and \textbf{\(h\)} is a physical constant known as Planck's constant, which is approximately \textbf{6.626 x 10^-34 joule seconds}.

In simpler terms, light that looks blue or violet to our eyes carries more energy per photon than red or yellow light. This is why ultraviolet light, which has an even shorter wavelength than violet light, can be harmful to our skin—it has more energy and can cause more damage at a molecular level.

ROY G. BIV is a mnemonic that helps us remember the order of colors in the visible light spectrum: Red, Orange, Yellow, Green, Blue, Indigo, and Violet. Not only does this acronym tell us the sequence of colors as we perceive them in a rainbow, but it also implicitly indicates the order of their wavelengths and energies.

From ROY G. BIV, we understand that red light has the longest wavelength and subsequently the lowest frequency and energy. As we move through the colors towards violet, wavelengths shorten, frequencies increase, and likewise, energies rise. So this catchy acronym isn't just a list of colors: it's also a gradient of optical properties.

The visible spectrum refers to the portion of the electromagnetic spectrum that the human eye can perceive. This range of wavelengths spans approximately from 380 nanometers (violet) to 750 nanometers (red).

Inside the visible spectrum, each color corresponds to a specific wavelength range. Red light, on the one end, has wavelengths around 625 to 750 nanometers. Moving down the spectrum, each color transitions smoothly into the next—orange, yellow, green, and blue—until we reach violet, with its wavelengths around 380 to 450 nanometers.

These colors combine to give us the white light we usually see. When light passes through a prism or droplets in the atmosphere (like during a rain shower), it splits into its constituent colors, creating a rainbow. This dispersion happens because different wavelengths bend by different amounts upon passing through a medium, beautifully revealing the colors we recognize as the visible spectrum.