Although the term is used in the field of optics to describe light and other electromagnetic waves, dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, and in gravity waves (ocean waves). Within optics, dispersion is a property of telecommunication signals along transmission lines (such as microwaves in coaxial cable) or the pulses of light in optical fiber.

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In the technical terminology of gemology, dispersion is the difference in the refractive index of a material at the B and G (686.7 nm and 430.8 nm) or C and F (656.3 nm and 486.1 nm) Fraunhofer wavelengths, and is meant to express the degree to which a prism cut from the gemstone demonstrates "fire". Fire is a colloquial term used by gemologists to describe a gemstone's dispersive nature or lack thereof. Dispersion is a material property. The amount of fire demonstrated by a given gemstone is a function of the gemstone's facet angles, the polish quality, the lighting environment, the material's refractive index, the saturation of color, and the orientation of the viewer relative to the gemstone.[10][11]

In photographic and microscopic lenses, dispersion causes chromatic aberration, which causes the different colors in the image not to overlap properly. Various techniques have been developed to counteract this, such as the use of achromats, multielement lenses with glasses of different dispersion. They are constructed in such a way that the chromatic aberrations of the different parts cancel out.

However, our bodies associate blue light with daytime, so exposure to it when you’re trying to go to bed “pushes our internal clocks later, so that it’s harder to fall asleep and harder to wake up in the morning,” says Cathy Goldstein, associate professor of neurology at the University of Michigan Sleep Disorders Center.

Blue-light-blocking capability: Tinted lenses that block up to 90 percent of blue light | Anti-glare coating: Yes | Frame material: Metal | Prescription compatible: No

If you’d rather get glasses that only add a slightly darker tint to whatever you’re looking at, this two-pack of thick-rimmed glasses work well enough while being arguably more stylish (and very cheap).

Dispersion of lightNotes PDF

Blue-light-blocking capability: Orange-tinted lenses that block 100 percent of blue light | Anti-glare coating: Yes | Frame material: Plastic | Prescription compatible: No, but goes over prescription glasses

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For visible light, refraction indices n of most transparent materials (e.g., air, glasses) decrease with increasing wavelength λ:

At the interface of such a material with air or vacuum (index of ~1), Snell's law predicts that light incident at an angle θ to the normal will be refracted at an angle arcsin(⁠sin θ/n⁠). Thus, blue light, with a higher refractive index, will be bent more strongly than red light, resulting in the well-known rainbow pattern.

Infield’s aptly named Terminator UV-400 glasses are great for comfort and blocking out nearly 100 percent of blue light. They’re cheaper than most other glasses with orange lenses I found, and their wraparound design provides more coverage for your eyes than lenses that cover only the front.

The most familiar example of dispersion is probably a rainbow, in which dispersion causes the spatial separation of a white light into components of different wavelengths (different colors). However, dispersion also has an effect in many other circumstances: for example, group-velocity dispersion causes pulses to spread in optical fibers, degrading signals over long distances; also, a cancellation between group-velocity dispersion and nonlinear effects leads to soliton waves.

In the case of multi-mode optical fibers, so-called modal dispersion will also lead to pulse broadening. Even in single-mode fibers, pulse broadening can occur as a result of polarization mode dispersion (since there are still two polarization modes). These are not examples of chromatic dispersion, as they are not dependent on the wavelength or bandwidth of the pulses propagated.

Refractionof lightthroughprism

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Material dispersion can be a desirable or undesirable effect in optical applications. The dispersion of light by glass prisms is used to construct spectrometers and spectroradiometers. However, in lenses, dispersion causes chromatic aberration, an undesired effect that may degrade images in microscopes, telescopes, and photographic objectives.

An everyday example of a negatively chirped signal in the acoustic domain is that of an approaching train hitting deformities on a welded track. The sound caused by the train itself is impulsive and travels much faster in the metal tracks than in air, so that the train can be heard well before it arrives. However, from afar it is not heard as causing impulses, but leads to a distinctive descending chirp, amidst reverberation caused by the complexity of the vibrational modes of the track. Group-velocity dispersion can be heard in that the volume of the sounds stays audible for a surprisingly long time, up to several seconds.

Unlike the NoCry glasses, below, these don’t totally cover the sides of your face, and there’s a slight gap at the bottom so some blue light may get in. They’re more stylish than the NoCrys, but those can be placed over another pair of glasses, while these cannot.

where λ = 2πc/ω is the vacuum wavelength, and vg = dω/dβ is the group velocity. This formula generalizes the one in the previous section for homogeneous media and includes both waveguide dispersion and material dispersion. The reason for defining the dispersion in this way is that |D| is the (asymptotic) temporal pulse spreading Δt per unit bandwidth Δλ per unit distance travelled, commonly reported in ps/(nm⋅km) for optical fibers.

In particular, the dispersion parameter D defined above is obtained from only one derivative of the group velocity. Higher derivatives are known as higher-order dispersion.[6][7] These terms are simply a Taylor series expansion of the dispersion relation β(ω) of the medium or waveguide around some particular frequency. Their effects can be computed via numerical evaluation of Fourier transforms of the waveform, via integration of higher-order slowly varying envelope approximations, by a split-step method (which can use the exact dispersion relation rather than a Taylor series), or by direct simulation of the full Maxwell's equations rather than an approximate envelope equation.

All common transmission media also vary in attenuation (normalized to transmission length) as a function of frequency, leading to attenuation distortion; this is not dispersion, although sometimes reflections at closely spaced impedance boundaries (e.g. crimped segments in a cable) can produce signal distortion which further aggravates inconsistent transit time as observed across signal bandwidth.

In electromagnetics and optics, the term dispersion generally refers to aforementioned temporal or frequency dispersion. Spatial dispersion refers to the non-local response of the medium to the space; this can be reworded as the wavevector dependence of the permittivity. For an exemplary anisotropic medium, the spatial relation between electric and electric displacement field can be expressed as a convolution:[8]

In general, the refractive index is some function of the frequency f of the light, thus n = n(f), or alternatively, with respect to the wave's wavelength n = n(λ). The wavelength dependence of a material's refractive index is usually quantified by its Abbe number or its coefficients in an empirical formula such as the Cauchy or Sellmeier equations.

Glasses with lenses that wrap around the front of your face will prevent more blue light from getting in, whereas traditional glasses allow light to hit your eyes from all sides.

The Strategist’s carefully chosen and rigorously vetted flagship shopping guides. Learn about our methodology here, and find all our Best in Class guides here.

Blue-light-blocking glasses may have an anti-glare coating, which decreases the amount of light reflecting from your glasses to further reduce eye strain and make them more comfortable to use. This is especially handy during video calls when people are going to be looking at you for long periods of time, as that light gets reflected right back at your screen and can make your eyes look weird when on camera.

While I didn’t notice a huge difference while watching TV, these glasses made a noticeable difference when reading at night. To test this, I read a book on my iPad in a dark room, both with the glasses and without. The lenses dimmed the screen enough that I didn’t have to adjust the brightness in my iPad’s settings. Because the lenses are only slightly tinted, as opposed to being orange like the Infields, the effect won’t be nearly as strong, but they also don’t affect the colors of the screen as much.

As with blue-light-blocking glasses for adults, those designed for kids won’t solve issues related to eye strain. “If you’re looking at a book for five hours a day, you’re going to have a lot of eye strain, and there’s no blue light coming from that,” says Milan Ranka, an ophthalmologist at Pediatric Ophthalmic Consultants in New York City. A better way for kids to relieve eye strain, according to Ranka, is to follow the same guidance given to adults. “For every 20 minutes you’re doing something, look 20 feet away for 20 seconds,” says Ranka. “I tell my 6-, 7-, and 8-year-old patients to look out the window every 15 to 20 minutes. Look for a tree and blink your eyes a few times.”

Updated on May 9, 2025We swapped in an updated model of the Sleep ZM Clip-On Blue Light Glasses. All our other picks are in stock.

If you’ve ever suffered from dry, irritated eyes or struggled to fall asleep after a long day of staring at your computer, you may have been tempted to purchase a pair of blue-light-blocking glasses. Blue light is found in nearly every light source, including the sun, and excessive exposure can harm your vision or prevent you from falling asleep.

I wore the NoCrys over a pair of Warby Parker readers and found them to be as effective as Infield’s glasses in dampening the harshness of my screen’s backlights. Despite having two layers of lenses over my face, I never noticed any issues with glare and found working on my laptop just as pleasant as with the similarly tinted Infield glasses. And though I was wearing two pairs of glasses, the added heft wasn’t that noticeable, as the NoCrys aren’t heavy at all and the rubber coating on the frames is comfortable.

In a perfect world, you’d start to avoid blue light from screens four hours before going to bed. But if you can’t tear yourself away from Instagram or the dreaded doomscroll before turning in, blue-light-blocking glasses can help. To find the most effective and stylish options, we scoured the internet and spoke with eye doctors and sleep experts about what they recommend.

Typically for astronomical observations, this delay cannot be measured directly, since the emission time is unknown. What can be measured is the difference in arrival times at two different frequencies. The delay Δt between a high-frequency νhi and a low-frequency νlo component of a pulse will be

It is possible to calculate the group velocity from the refractive-index curve n(ω) or more directly from the wavenumber k = ωn/c, where ω is the radian frequency ω = 2πf. Whereas one expression for the phase velocity is vp = ω/k, the group velocity can be expressed using the derivative: vg = dω/dk. Or in terms of the phase velocity vp,

Applicationof dispersion of light

One caveat: Even if you’re ordering a nonprescription pair, any pair of these glasses will cost you at least $150, which is pricey. I’d recommend buying these only if you plan on wearing your glasses frequently; if you want a cheaper pair of stylish glasses, the AFNWQI glasses have a nice thick-rimmed look.

Every product is independently selected by (obsessive) editors. Things you buy through our links may earn us a commission.

Waveguides are highly dispersive due to their geometry (rather than just to their material composition). Optical fibers are a sort of waveguide for optical frequencies (light) widely used in modern telecommunications systems. The rate at which data can be transported on a single fiber is limited by pulse broadening due to chromatic dispersion among other phenomena.

Beyond simply describing a change in the phase velocity over wavelength, a more serious consequence of dispersion in many applications is termed group-velocity dispersion (GVD). While phase velocity v is defined as v = c/n, this describes only one frequency component. When different frequency components are combined, as when considering a signal or a pulse, one is often more interested in the group velocity, which describes the speed at which a pulse or information superimposed on a wave (modulation) propagates. In the accompanying animation, it can be seen that the wave itself (orange-brown) travels at a phase velocity much faster than the speed of the envelope (black), which corresponds to the group velocity. This pulse might be a communications signal, for instance, and its information only travels at the group velocity rate, even though it consists of wavefronts advancing at a faster rate (the phase velocity).

[Editor’s note: The exact glasses Jordan reviewed are no longer available, but this is a newer model of the same brand of clip-on glasses.]

Dispersion control is also important in lasers that produce short pulses. The overall dispersion of the optical resonator is a major factor in determining the duration of the pulses emitted by the laser. A pair of prisms can be arranged to produce net negative dispersion, which can be used to balance the usually positive dispersion of the laser medium. Diffraction gratings can also be used to produce dispersive effects; these are often used in high-power laser amplifier systems. Recently, an alternative to prisms and gratings has been developed: chirped mirrors. These dielectric mirrors are coated so that different wavelengths have different penetration lengths, and therefore different group delays. The coating layers can be tailored to achieve a net negative dispersion.

What isdispersion of light

In this case, the medium is said to have normal dispersion. Whereas if the index increases with increasing wavelength (which is typically the case in the ultraviolet[4]), the medium is said to have anomalous dispersion.

Why doesdispersion of lightoccur in aprism

The result of GVD, whether negative or positive, is ultimately temporal spreading of the pulse. This makes dispersion management extremely important in optical communications systems based on optical fiber, since if dispersion is too high, a group of pulses representing a bit-stream will spread in time and merge, rendering the bit-stream unintelligible. This limits the length of fiber that a signal can be sent down without regeneration. One possible answer to this problem is to send signals down the optical fibre at a wavelength where the GVD is zero (e.g., around 1.3–1.5 μm in silica fibres), so pulses at this wavelength suffer minimal spreading from dispersion. In practice, however, this approach causes more problems than it solves because zero GVD unacceptably amplifies other nonlinear effects (such as four-wave mixing). Another possible option is to use soliton pulses in the regime of negative dispersion, a form of optical pulse which uses a nonlinear optical effect to self-maintain its shape. Solitons have the practical problem, however, that they require a certain power level to be maintained in the pulse for the nonlinear effect to be of the correct strength. Instead, the solution that is currently used in practice is to perform dispersion compensation, typically by matching the fiber with another fiber of opposite-sign dispersion so that the dispersion effects cancel; such compensation is ultimately limited by nonlinear effects such as self-phase modulation, which interact with dispersion to make it very difficult to undo.

Look Optic is a direct-to-consumer brand that makes handsome reading glasses (the design team is made up of Oliver Peoples alumni). It offers blue-light protection in some of its most popular styles — either with magnification or without. These particular frames come in two colors, and you can choose a magnification between +0.0 and +3.0. If these frames don’t match your particular style, Look Optic has five other similarly priced styles.

Pulsars are spinning neutron stars that emit pulses at very regular intervals ranging from milliseconds to seconds. Astronomers believe that the pulses are emitted simultaneously over a wide range of frequencies. However, as observed on Earth, the components of each pulse emitted at higher radio frequencies arrive before those emitted at lower frequencies. This dispersion occurs because of the ionized component of the interstellar medium, mainly the free electrons, which make the group velocity frequency-dependent. The extra delay added at a frequency ν is

While you don’t need a prescription to get a pair of these glasses, some blue-light-blocking lenses and frames work with prescription lenses, so you won’t have to deal with having two pairs. Other pairs can be worn over a pair of prescription lenses, or clipped directly onto them.

Blue-light-blocking capability: Tinted lenses that block up to 90 percent of blue light | Anti-glare coating: Yes | Frame material: Plastic | Prescription compatible: No

Rewriting the above equation in terms of Δt allows one to determine the DM by measuring pulse arrival times at multiple frequencies. This in turn can be used to study the interstellar medium, as well as allow observations of pulsars at different frequencies to be combined.

In optics, one important and familiar consequence of dispersion is the change in the angle of refraction of different colors of light,[2] as seen in the spectrum produced by a dispersive prism and in chromatic aberration of lenses. Design of compound achromatic lenses, in which chromatic aberration is largely cancelled, uses a quantification of a glass's dispersion given by its Abbe number V, where lower Abbe numbers correspond to greater dispersion over the visible spectrum. In some applications such as telecommunications, the absolute phase of a wave is often not important but only the propagation of wave packets or "pulses"; in that case one is interested only in variations of group velocity with frequency, so-called group-velocity dispersion.

Most often, chromatic dispersion refers to bulk material dispersion, that is, the change in refractive index with optical frequency. However, in a waveguide there is also the phenomenon of waveguide dispersion, in which case a wave's phase velocity in a structure depends on its frequency simply due to the structure's geometry. More generally, "waveguide" dispersion can occur for waves propagating through any inhomogeneous structure (e.g., a photonic crystal), whether or not the waves are confined to some region.[dubious – discuss] In a waveguide, both types of dispersion will generally be present, although they are not strictly additive.[citation needed] For example, in fiber optics the material and waveguide dispersion can effectively cancel each other out to produce a zero-dispersion wavelength, important for fast fiber-optic communication.

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Blue-light-blocking capability: Clear lenses that block nearly 90 percent of blue light | Anti-glare coating: None | Frame material: Plastic | Prescription compatible : No

Whitelight prism

and the dispersion measure (DM) is the column density of free electrons (total electron content) – i.e. the number density of electrons ne integrated along the path traveled by the photon from the pulsar to the Earth – and is given by

When a broad range of frequencies (a broad bandwidth) is present in a single wavepacket, such as in an ultrashort pulse or a chirped pulse or other forms of spread spectrum transmission, it may not be accurate to approximate the dispersion by a constant over the entire bandwidth, and more complex calculations are required to compute effects such as pulse spreading.

If you’re worried about screens affecting your kid’s sleep schedule, blue-light-blocking glasses are made for children’s faces too. They can help kids with the same side effects of screen time that many adults experience — namely, poor sleep and migraines. This pair from Felix Gray comes in two sizes — small (ages 4 to 8) and large (ages 9 to 13) — and four colors.

Many blue-light-blocking glasses have an orange or yellow tint that is supposed to absorb the blue light while allowing other light to pass through. Generally, the darker the lenses on a pair of blue-light-blocking glasses, the more blue light is blocked. While there are clear or less obviously tinted blue-light-blocking lenses, they won’t filter as much blue light as darker options. If you’re working with visuals, whether video or photo editing, illustrating, or graphic design, it’s best to avoid glasses with more orange hues and do that work during the day.

When dispersion is present, not only the group velocity is not equal to the phase velocity, but generally it itself varies with wavelength. This is known as group-velocity dispersion and causes a short pulse of light to be broadened, as the different-frequency components within the pulse travel at different velocities. Group-velocity dispersion is quantified as the derivative of the reciprocal of the group velocity with respect to angular frequency, which results in group-velocity dispersion = d2k/dω2.

While the Infields are the most effective at blocking out blue light, their orange hue may be off-putting to those who want to use their glasses while editing pictures and videos or watching TV. I tested them out by watching a show at 80 percent brightness as well as getting some writing done on my laptop. In both cases, these lenses made enough of a different that my eyes felt less strained than usual after a reading session. I like the plain black frames, but if you prefer a different look, there are eight colors to choose from, and there are a few combinations you can select.

Because of the Kramers–Kronig relations, the wavelength dependence of the real part of the refractive index is related to the material absorption, described by the imaginary part of the refractive index (also called the extinction coefficient). In particular, for non-magnetic materials (μ = μ0), the susceptibility χ that appears in the Kramers–Kronig relations is the electric susceptibility χe = n2 − 1.

Prism dispersion

Dispersion of lightthroughprismexperiment

If you’re picky about your frames, Warby Parker has a large collection of unique styles to suit any face, and you can do a virtual try-on of any frame using the company’s app. After doing this myself, I got a pair of Ellington frames (in gold) to test out. I’m picky about my glasses, as I feel most accentuate the parts of my face I don’t like, but these frames looked the same on me in person as they did in my virtual try-on. They’re also comfy to wear, and the pair I’ve been testing (which only had blue-light-blocking, not prescription lenses) made things like reading on my iPad or watching a movie at night noticeably less problematic for falling asleep.

There are different frame materials to choose from including wire, plastic, and acetate. If you don’t already wear prescription or reading glasses, any pair of blue-light-blocking glasses will be easy to pick up and use. But if you already have glasses, you’ll want to look for either a prescription pair, reading glasses with blue-light-blocking capabilities, or something that will clip on or fit over the top of your existing glasses.

Blue-light-blocking capability: Yellow- or orange-tinted lenses that block from 87 to 99 percent of blue light | Anti-glare coating: Yes | Frame material: Metal clip | Prescription compatible: No

Blue-light-blocking capability: Yellow-tinted lenses that block 50 percent of blue light | Anti-glare coating: Yes | Frame material: Plastic | Prescription compatible: Yes

• Cathy Goldstein, associate professor of neurology at the University of Michigan Sleep Disorders Center• Rahul Khurana, ophthalmologist and former clinical spokesperson for the American Academy of Ophthalmology• Milan Ranka, ophthalmologist at Pediatric Ophthalmic Consultants

If you already wear prescription glasses, you might be interested in blue-light-blocking clip-ons, like this pair, that attach to your existing frames. The yellow shuts out 87 percent of blue light. The orange blocks 99 percent. One enthusiastic Amazon reviewer reports that they “fit securely onto my night glasses without having an obnoxious or clunky nose guard that I’ve seen in other competitive brands” and do “a great job staying in place on my frames.” Another reviewer reports experiencing significantly less eye strain while watching TV or using a computer and says the glasses allow them to sleep better at night.

I wore them at night while watching a couple shows and getting some writing done, and while the orange hue was noticeable on both screens, it didn’t look so terrible that I wanted to take off the glasses. In exchange for adding an orange filter to everything, the Infields did make both screens feel less harsh to look at, but I found myself having to squint for a second or two after removing them.

NoCry’s blue-light-blocking glasses are great for blocking out nearly 100 percent of blue light. They’re cheaper than most other glasses with orange lenses that I could find, and their wrap-around design totally covers the sides of your face and leaves very little gap at the bottom, providing more coverage for your eyes than lenses that cover only the front. They also have enough room to fit over prescription or reading glasses, though you can wear them on their own as well.

If a light pulse is propagated through a material with positive group-velocity dispersion, then the shorter-wavelength components travel slower than the longer-wavelength components. The pulse therefore becomes positively chirped, or up-chirped, increasing in frequency with time. On the other hand, if a pulse travels through a material with negative group-velocity dispersion, shorter-wavelength components travel faster than the longer ones, and the pulse becomes negatively chirped, or down-chirped, decreasing in frequency with time.

Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.[1] Sometimes the term chromatic dispersion is used to refer to optics specifically, as opposed to wave propagation in general. A medium having this common property may be termed a dispersive medium.

In general, for a waveguide mode with an angular frequency ω(β) at a propagation constant β (so that the electromagnetic fields in the propagation direction z oscillate proportional to ei(βz−ωt)), the group-velocity dispersion parameter D is defined as[5]

All light is measured in nanometers (nm), and blue-light wavelengths that can have the most impact on your melatonin levels (and thus affect your sleep) range from 400 to 500 nm, though blue-light wavelengths start at 200 nm. Blue-light-blocking glasses work by reflecting those wavelengths away from the lenses to stop them from reaching your eyes. (Note that, despite emitting blue light, most consumer tech is not harmful and there is no scientific evidence that digital devices can damage your eyes.)

The most commonly seen consequence of dispersion in optics is the separation of white light into a color spectrum by a prism. From Snell's law it can be seen that the angle of refraction of light in a prism depends on the refractive index of the prism material. Since that refractive index varies with wavelength, it follows that the angle that the light is refracted by will also vary with wavelength, causing an angular separation of the colors known as angular dispersion.

where the kernel f i k {\displaystyle f_{ik}} is dielectric response (susceptibility); its indices make it in general a tensor to account for the anisotropy of the medium. Spatial dispersion is negligible in most macroscopic cases, where the scale of variation of E k ( t − τ , r ′ ) {\displaystyle E_{k}(t-\tau ,r')} is much larger than atomic dimensions, because the dielectric kernel dies out at macroscopic distances. Nevertheless, it can result in non-negligible macroscopic effects, particularly in conducting media such as metals, electrolytes and plasmas. Spatial dispersion also plays role in optical activity and Doppler broadening,[8] as well as in the theory of metamaterials.[9]

You can get wire-framed glasses through Warby Parker, but they’re pricey. These glasses are significantly cheaper and still have a stylish, understated look that feels lightweight. Although they don’t block out as much blue light as the Infields, they’re effective and comfortable.

But will filtering out blue light help with the digital eye strain that comes from extended time in front of a screen? Rahul Khurana, an ophthalmologist and former clinical spokesperson for the American Academy of Ophthalmology, says that digital eye strain and the negative effects of blue light on your eyes are two separate concerns. “We keep on thinking about blue light from our computers and smartphones, but the reality is that we get more exposure to blue light from the sun.” Essentially, it’s not the blue light that’s making your eyes feel bad after a day of staring at the computer. It’s staring at a screen for hours without breaks. That’s why Khurana doesn’t recommend any special eyewear for daily computer use. “Ultimately, I’m not really sure how it’s going to help with digital eye strain, which is what’s bothering people,” he says, explaining that the eye strain most people experience isn’t necessarily digital. It can occur “whenever you focus on anything — from reading a book, looking at a screen, or watching TV.” It can be alleviated by shifting your eyes every 20 minutes or so to something that’s 20 feet away for at least 20 seconds, he says. If that doesn’t help, Khurana recommends artificial tears to help lubricate dry eyes. In the end, he says you don’t need to wear blue-light-blocking glasses during the day.

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