How this instrument works
Frequency counts how many wave crests pass a fixed point each second, in hertz. For light in vacuum, that count is fixed the instant it leaves its source and does not change again, no matter what the beam later travels through. Wavelength, by contrast, is a distance between crests, and distance depends on how fast the wave is moving through whatever it currently occupies. Because speed equals frequency times wavelength, and light's vacuum speed c is a fixed 299,792,458 metres per second, dividing that constant by a vacuum wavelength recovers frequency directly: f = c ⁄ λ. Halve λ and f doubles; there is no other way for the product to stay put.
This is exactly why fibre-optic networks assign channels by frequency rather than by wavelength. A signal entering a glass core slows to roughly two-thirds of c, so its wavelength inside that glass is not the number printed on the transmitter's label — but its frequency never moves, because frequency is set once at the source and glass has no power to change how often crests are emitted. The ITU-T's dense wavelength-division multiplexing grid consequently spaces its channels in terahertz — 193.1 THz, 193.2 THz, and onward — a scheme that stays correct whether the light is sitting in a vacuum, a silica fibre, or an erbium amplifier, which a wavelength-based grid could not promise.
The formula's blind spot is that it only accepts a vacuum, or air-approximated, wavelength as input. Feed it a wavelength already measured inside glass, water, or a coating, and the answer comes out wrong by exactly that medium's refractive index, because c ⁄ λ silently assumes the wave in front of you is travelling at c. Divide the in-medium wavelength by its refractive index first, or start from a vacuum figure, and the result again matches what a frequency counter would report.
- Enter the light's vacuum wavelength into the Wavelength field, in nanometres by default — 550 nm sits near the middle of the visible band.
- Switch the Wavelength unit menu to micrometres or metres for infrared or radio-scale sources instead of retyping zeros.
- Read the result in the Frequency field, which reports hertz by default and can be switched to kilohertz, megahertz, or gigahertz for a shorter number.
- For very large frequencies, note the digit count rather than reading every place: visible light lands in the hundreds of trillions of hertz.
- Check the direction of any change: shortening Wavelength always raises Frequency, in exact inverse proportion, never the reverse.
Worked example — 550 nm green light
Set Wavelength to 550 nm, close to where daylight vision is most sensitive. In metres that is 5.5 × 10⁻⁷. Substituting into f = c ⁄ λ: f = 299,792,458 ⁄ (5.5 × 10⁻⁷) = 545,077,196,364,000 Hz — the same figure written as 545.077196364 THz, or 545,077.196364 GHz on this instrument's own unit menu.
That number is worth holding onto as an anchor. Red light at 700 nm works out to a lower 428,274,940,000,000 Hz, about 428.27 THz, while violet at 400 nm works out to a higher 749,481,145,000,000 Hz, about 749.48 THz — confirming that across the visible band, shorter wavelength always means higher frequency, the opposite of the everyday intuition that longer waves are the fast ones.
Questions
Why does shorter wavelength mean higher frequency for light?
Because speed is fixed. For any wave, speed equals frequency times wavelength; hold that product constant, as vacuum does for light at exactly 299,792,458 m/s, and the two factors must move in opposite directions. Violet at 400 nm reaches 749.48 THz while red at 700 nm reaches only 428.27 THz — the shorter length is paired with the faster oscillation, not the slower one.
Does light's frequency change when it enters glass or water?
No. Frequency is set at the source and stays fixed as light crosses any boundary; what changes inside the medium is speed, which drops to roughly c divided by the refractive index, so wavelength shrinks to match. This is why colour, which the eye reads from frequency far more reliably than from a shifting in-medium length, does not change when light passes from air into a lens.
Why do fibre-optic and radio engineers specify channels by frequency?
Because frequency survives the trip through any medium unchanged, while wavelength does not. A dense wavelength-division multiplexing grid spaced by wavelength would drift as light moved between vacuum, fibre core, and amplifier; spacing it in frequency, as the ITU-T grid does at 100 GHz or 50 GHz intervals starting near 193.1 THz, keeps every channel exactly where it was defined regardless of what the light is currently travelling through.
What frequency corresponds to the edges of visible light?
Roughly 400 THz at the red edge, near 700 nm, up to about 790 THz at the violet edge, near 380 nm. This instrument's own vectors confirm two interior points: 700 nm gives 428.27 THz and 400 nm gives 749.48 THz, both comfortably inside that visible span and each recoverable from f = c ⁄ λ alone.
Can I enter an in-medium wavelength directly, like one measured inside a fibre core?
Only after dividing it by that medium's refractive index first, since f = c ⁄ λ assumes the wavelength given is a vacuum or near-vacuum figure. A wavelength already shortened by glass fed in unmodified returns a frequency too low by the same factor, because the formula has no way to know the light was ever slowed down.
How is optical frequency actually measured, rather than just calculated?
With a frequency comb, a laser pulsed so regularly that its spectrum forms an evenly spaced ladder of exact frequencies, each one countable against a microwave atomic clock. Before this technique, comparing visible-light frequencies near 500 THz to the caesium clocks that define the second required an unwieldy chain of intermediate oscillators; the comb, developed in the late 1990s and recognised with a share of the 2005 Nobel Prize in Physics, collapsed that chain into one instrument and now underlies optical atomic clocks accurate to better than a second over the age of the universe.