Frequency of Light Calculator

Calculating the frequency of light may be a simple mathematical operation, but it opens the door to a complete understanding of the variegated nature of electromagnetic radiation. Join Omni in a short exploration of light. Keep reading if you want to learn:

• What is light?
• How to calculate the frequency of light with a given wavelength: the formula for the frequency of light.
• The types of electromagnetic radiation, with particular attention to visible light and its frequency.
• How to calculate the frequency of visible light in a worked example.

What are you waiting for? Let's go!

The answer is... complicated! Let's shed some light on the topic.

What we usually call "light" is only a portion of the electromagnetic spectrum. The electromagnetic spectrum represents all the possible types of electromagnetic radiation. We better explain these last two words:

• Radiation: with the word radiation we mean the transmission of energy by means of waves or particles.
• Electromagnetic: describes a phenomenon that depends on both electricity and magnetism.

That's true: light is an electromagnetic phenomenon: electric and magnetic fields are deeply interconnected, and when one propagates in space, the other follows (perpendicular and with a phase difference). The result of this propagation is the electromagnetic radiation.

The frequency of the oscillation of the electromagnetic field determines the frequency of the radiation. Notice that the speed of propagation is the same for all types of electromagnetic radiation.

What about photons?

In quantum physics, the description of electromagnetic radiation uses photons, massless particles. Photons are the quanta of the electromagnetic field, its fundamental components. In this framework, photons carry energy (a quantized amount) and travel in an undulatory fashion at the speed of light while still sharing some aspect of a corpuscular nature, as we can observe when we detect single photons.

Photons are much easier to visualize, as we can imagine they move with a given frequency. How do we calculate the frequency of light? How are the frequency and the wavelength of light related?

If you want to know how to calculate the frequency of light with a wavelength of your choice, you are in the right place! In the previous section, we mentioned that the electromagnetic field, or the photons oscillates: every oscillatory movement is characterized by two fundamental quantities:

• The frequency: the inverse of the time required to return to the initial status; and
• The wavelength: the distance between two points sharing the same amplitude (for example two peaks).

To calculate the frequency of light from the wavelength, we need to know light's propagation speed. Luckily for us, this quantity is well known, as it defines the speed limit of the Universe, and we thoroughly quantified it in the past. The speed of light in the vacuum is exactly:

Now we can introduce the formula for the frequency of light calculated with the wavelength:

where:

• $\nu$ — Frequency in hertz ($\rm Hz$); and
• $\lambda$ — Wavelength in meters.

This operation is valid for every wave-like phenomena: discover more at our wavelength to frequency calculator.

What is the frequency of visible light? And of the other types of electromagnetic radiation?

Electromagnetic radiation comes in many flavors. Let's explore them using the wavelength as our lead. First, let's meet radiation with a very small wavelength: let's talk of ionizing radiations.

Ionizing radiation

At one end of the electromagnetic spectrum, we find photons with a wavelength in the atomic and subatomic scale. These photons are the most energetic, as you can see at our photon energy calculator: so much that they can cause significant damage to other atoms or materials by forcefully knocking electrons away from the negative cloud surrounding the nuclei, or by breaking the chemical bonds in molecules.

• For wavelengths smaller than $10^{-12}\ \mathrm{m} = 1\ \mathrm{pm}$ (picometer), we find gamma rays, the most dangerous type of electromagnetic radiation. Only extremely energetic phenomena can generate gramma photons: lightning, supernovae, or nuclear explosions.

• For wavelengths between $1 \ \mathrm{pm}$ and $10^{-9}\ \mathrm{m} = 1\ \mathrm{nm}$ (nanometer), we find X-rays. The high energy of X-rays is why we use them thoroughly in medical imaging (and not only), but they still harbor some degree of risk. This is why you'll wear lead protection over sensitive parts of your body during routine radiography!

What comes next? We move into the "safe" area of the electromagnetic spectrum, where we meet ultraviolet radiation.

Ultraviolet light

Ultraviolet (UV) light is still energetic but not enough to be downright dangerous. It remains preferable to shield yourself a bit (Earth helps us by filtering most of the UV light coming from the Sun) using sunscreen and appropriate protection. Prolonged exposure to intense UV light can still damage the chemical bonds of the molecule in your body, increasing, for example, the likelihood of developing skin cancer.

UV light belongs to the range of wavelength between $1\ \mathrm{nm}$ and $\text{380-400}\ \mathrm{nm}$. In this range, we can identify four subdivisions:

• Extreme ultraviolet light;
• Far ultraviolet light;
• Middle ultraviolet light; and
• Near ultraviolet light.

Extreme ultraviolet light is at the threshold of ionizing radiations and is commonly used as a germicide. On the other hand, near-ultraviolet has relatively low energy and begins to get close to what humans can perceive: many animals have partial sensitivity to this radiation. By the way, do you know why it's called "ultraviolet"? Because it comes after (ultra) the violet: yes, we are about to enter the realm of visible light.

Visible light

Visible light, what we call light in our everyday conversation, is the portion of the electromagnetic spectrum that causes activation of our sensory cells in the eyes. We perceive different wavelengths as different colors, creating a rainbow. The first color is violet, corresponding to roughly a wavelength of $480\ \mathrm{nm}$. We then pass blue, green, yellow, and orange till we end with red. Red light has the lowest energy (hence the greatest wavelength) that our eyes can perceive, at about $780\ \mathrm{nm}$. We will discuss the frequency of visible light in the next section.

Infrared radiation

At wavelengths greater than the one defining red light, we meet the infrared radiation. This low-energetic form of light is mostly responsible for heating: if you know the feeling of warmth in your skin when exposed to sunlight, even in the winter, then you know the effect of infrared radiation. Infrared light has wavelength between $780\ \mathrm{nm}$ and $1\ \mathrm{mm}$.

What comes next are microwaves and radio waves (yes: radio waves are light!).

• Microwaves have wavelengths between $1 \ \mathrm{mm}$ and $1\ \mathrm{m}$. They carry low energy but interact in specific ways with certain molecules, causing them to vibrate and heating them: this is the principle between your microwave oven.

• Radio waves have wavelengths longer than $1\ \mathrm{m}$, without necessarily a boundary, though after a million meters of wavelength, photons start to carry negligible amounts of energy.

Let's try our hand at the formula to calculate the frequency of light in the visible range. Say that you choose a wavelength of $500\ \mathrm{nm}$. How do we find the corresponding frequency?

Divide the speed of light by the wavelength after converting it to meters:

Then:

All the frequencies of visible light fall in the range of hundreds of terahertz (e.g., $599.6\ \mathrm{THz}$ corresponds to bright green). Higher frequencies would return increasingly blue and violet hues, while reducing the frequency would bring you to red shades.

The magenta problem

What is magenta? Magenta is the color in between red and blue, and it doesn't exist. Human brains are wired to mix colors and create hues from these mixtures. Imagine: you can mix yellow and blue and obtain green, which lies, by the way, in between them in the spectrum. However, the spectrum is not closed but more of a strip, with blue and red at the ends. Our brain closes this strip, joining these two colors with magenta: this color is not associated with any wavelength and exists only in our brains!

Our frequency of light calculator shows you how the frequency and the wavelength of light are related. Insert one or the other, and let us do the math. If possible, we will print to which region of the spectrum the inserted radiation belongs, to the sub-region level.

If you input a wavelength or frequency in the visible range, we will also print a "sample" of that color in a rectangle!

To calculate the frequency of light from the wavelength, follow these easy steps:

1. Note the speed of light in m/s: 299,792,458 m/s.
2. Convert the wavelength into meters.
3. Divide the speed of light by the wavelength.
4. If the result has a large exponent in scientific notation, use the metric prefixes to find a more comfortable unit (THz, GHz, ...).

The frequency of blue light is about 680 THz, which corresponds to around 440 nm. This is not the highest possible frequency for visible light. The most extreme violet radiation can reach almost 790 THz, corresponding to 480 nm.

Ultraviolet and infrared are the regions bordering the visible part of the electromagnetic spectrum.

• Infrared corresponds to greater wavelengths than visible light and lies on the red side of the spectrum. Infrared light is low in energy and contributes to heating.
• Ultraviolet corresponds to shorter wavelengths than visible light. Its energy is higher than the one of blue light and can quickly become dangerous for living organisms.

The color with the lowest frequency is red, with a wavelength of about 780 nm (or frequencies of around 380 THz). Having the lowest frequency implies that its energy is also the lowest. The fact that we associate red with warmer temperatures depends on our psychology and daily experience: most warm objects we can perceive have colors in the yellow-orange-red section of the visible spectrum.