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 us 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!
What is light?
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?
How to calculate the frequency of light from the wavelength?
The frequency of light is related to its wavelength through the speed of light. The formula for the frequency of light is:
f = c / λ
- f — the frequency of the light, measured in hertz (Hz);
- c — the speed of light in vacuum, c = 2.99792458 × 108 m/s; and
- λ — the wavelength of the light, measured in meters (m).
Because the speed of light is constant, the frequency and wavelength are inversely proportional: the shorter the wavelength, the higher the frequency. If light travels through a medium other than vacuum, replace c with the speed of light in that medium, v = c / n, where n is the refractive index.
The energy carried by each photon follows directly from the frequency through the Planck relation E = h × f, where h = 6.62607 × 10−34 J·s is the Planck constant.
The types of electromagnetic radiation
The electromagnetic spectrum is divided into regions by wavelength (or, equivalently, by frequency). From the longest wavelength (lowest frequency) to the shortest wavelength (highest frequency):
| Region | Wavelength | Frequency |
|---|---|---|
| Radio waves | > 1 m | < 300 MHz |
| Microwaves | 1 mm – 1 m | 300 MHz – 300 GHz |
| Infrared (IR) | 700 nm – 1 mm | 300 GHz – 430 THz |
| Visible light | 400 – 700 nm | 430 – 750 THz |
| Ultraviolet (UV) | 10 – 400 nm | 750 THz – 30 PHz |
| X-rays | 0.01 – 10 nm | 30 PHz – 30 EHz |
| Gamma rays | < 0.01 nm | > 30 EHz |
Calculate the frequency of light in the visible region of the spectrum: an example
The human eye sees a narrow band of the spectrum: visible light, with wavelengths roughly between 400 nm and 700 nm. Let's calculate the frequency of green light with a wavelength of λ = 500 nm.
- Convert the wavelength to meters: λ = 500 nm = 500 × 10−9 m = 5 × 10−7 m.
- Apply the formula: f = c / λ = (2.998 × 108 m/s) / (5 × 10−7 m).
- The result: f ≈ 5.996 × 1014 Hz ≈ 599.6 THz.
The visible spectrum corresponds approximately to:
- Red light (λ ≈ 700 nm): f ≈ 428 THz
- Green light (λ ≈ 500 nm): f ≈ 600 THz
- Violet light (λ ≈ 400 nm): f ≈ 750 THz
How to use our frequency of light calculator
- Choose what you want to enter: wavelength or frequency.
- Type the value and pick the unit. Both the metric system (nm, μm, pm, Å, mm, cm, m) and the American system (mil, inch, foot) are supported for wavelength; frequency can be entered in Hz, kHz, MHz, GHz, THz, or PHz.
- If the light travels through a medium other than vacuum (for example water, n ≈ 1.33, or glass, n ≈ 1.5), enter the refractive index. Leave it at 1 for vacuum or air.
- Read the results: the calculator returns the frequency (in Hz, THz, and PHz), the period, the angular frequency, the wavelength in several units, the wavenumber, the photon energy, and the region of the electromagnetic spectrum.
Frequently Asked Questions
What is the frequency of visible light?
Visible light has frequencies between approximately 430 THz (red, ~700 nm) and 750 THz (violet, ~400 nm). That is, between 4.3 × 1014 Hz and 7.5 × 1014 Hz.
How do I calculate the frequency of light from its wavelength?
Divide the speed of light by the wavelength: f = c / λ. For example, for λ = 600 nm, f = (3 × 108) / (600 × 10−9) ≈ 5 × 1014 Hz = 500 THz.
Does the frequency of light change in a medium?
No. When light enters a medium such as water or glass, its speed and wavelength decrease, but its frequency stays the same. The colour we perceive is tied to the frequency, which is why a beam keeps its colour underwater.
What is the relationship between frequency and energy?
The energy of a photon is directly proportional to its frequency: E = h × f, where h is the Planck constant. Higher-frequency light (blue, UV, X-rays) carries more energy per photon than lower-frequency light (red, infrared, radio).
What units are used for the frequency of light?
The SI unit of frequency is the hertz (Hz). Because the frequency of light is very large, it is often expressed in terahertz (1 THz = 1012 Hz) or petahertz (1 PHz = 1015 Hz).