Visible light

Visible light is the part of the electromagnetic spectrum that produces vision, conventionally taken as wavelengths in vacuum from 380 nm (violet) to 780 nm (deep red). The corresponding frequencies are 789 THz down to 384 THz, and photon energies run from 3.26 eV to 1.59 eV. The limits are soft: the eye's sensitivity falls smoothly at both ends, and colorimetric tables from the CIE extend from 360 nm to 830 nm. Shorter wavelengths are ultraviolet and longer ones infrared.

Conversions

Wavelength, frequency and photon energy are related by

$$\nu = \frac{c}{\lambda}, \qquad E\,[\text{eV}] = \frac{1239.84}{\lambda\,[\text{nm}]}.$$

A green 532 nm laser, for example, has a frequency of 564 THz and a photon energy of 2.33 eV; see wavelength, frequency and wavenumber for the general conversions. Wavelengths are usually quoted in air in older optical tables (such as the 632.8 nm helium-neon line) and differ from vacuum values by about 0.03%.

Colours and the eye

Approximate colour bands are:

The boundaries are conventions; perceived colour also depends on surroundings, intensity and adaptation, and many colours (purple, white, brown) have no single wavelength. Colour vision uses three cone types peaking roughly in the blue, green and yellow-green. Under daylight (photopic) conditions the combined luminous efficiency $V(\lambda)$ peaks at 555 nm; under dark-adapted (scotopic) rod vision it peaks at 507 nm, and a maximum efficacy of about 1700 lm/W applies instead of 683 lm/W.

The shape of $V(\lambda)$ explains why equal powers look very different. With $V(650\ \text{nm}) = 0.107$ and $V(532\ \text{nm}) \approx 0.88$, a 532 nm beam appears about 8.3 times brighter than a 650 nm beam of the same power, and at 700 nm the sensitivity has fallen to 0.0041, 26 times below its value at 650 nm. Photometric units that follow from this weighting are covered under brightness.

Sources and detectors

Sunlight above the atmosphere peaks in the visible; a 5772 K blackbody, a close model of the Sun, has its spectral peak (per unit wavelength) at 502 nm and emits about 46% of its power between 380 and 780 nm. Common visible laser lines include 405 nm and 450 nm from gallium nitride diodes, 532 nm from frequency-doubled Nd lasers, 632.8 nm from helium-neon lasers and 635–660 nm from red diodes. Silicon photodiodes cover the whole visible band; the 1.12 eV silicon bandgap corresponds to a cutoff near 1107 nm. Ordinary crown glass such as N-BK7 is transparent across the visible, with $n_d = 1.5168$ and an Abbe number of 64.2, and its dispersion across this band is what a prism displays.

Where the range matters

Display and lighting engineering, colorimetry, microscopy and machine vision are built around the visible band. Visible lasers are also the natural choice for alignment: an infrared beam must be traced with viewer cards or cameras, whereas a visible beam can be seen on any surface. Many laser safety rules assume that the blink and aversion response, about 0.25 s, limits exposure to visible beams; this is the basis of the 1 mW limit for Class 2 lasers, and the protection does not apply to infrared beams, which are not seen at all.

Pitfalls

Radiometric power and perceived brightness are separate quantities: a detector calibrated in watts reads a 700 nm source correctly, while the eye underrates it by a large factor. Near 400 nm and near 700 nm, visibility falls so fast that small wavelength shifts change apparent brightness noticeably. Some "visible" sources, such as deep-red and violet LEDs, emit much of their power where the eye is insensitive, which a radiometric power rating does not reveal.

Common questions

What is the wavelength range of visible light?

About 380 nm to 780 nm in vacuum. Some references use 400–700 nm, which covers nearly all perceived brightness; some observers see a little beyond both ends at high intensity.

Which colour of light has the most energy?

Violet, since photon energy rises as wavelength falls: about 3.26 eV per photon at 380 nm against 1.59 eV at 780 nm.

Why does green look brightest?

The eye's photopic sensitivity peaks at 555 nm, in the green. At equal power a green source therefore produces more lumens than red or blue sources.

References: E. Hecht, Optics, 5th ed. (Pearson, 2017); G. Wyszecki, W. S. Stiles, Color Science, 2nd ed. (Wiley, 1982); CIE 015:2018, Colorimetry, 4th ed.