Still, these initiatives are small compared to the larger forces driving polarization. Democracies will need to rise to this challenge in new and determined ways if they are to swim successfully against the swelling global current of polarization.

We also found that patronage and corruption—two decidedly antidemocratic practices—can temporarily reduce polarization by helping politicians build very big tents. In the long term, however, the political rot that this causes frequently leaves voters disgusted with the traditional parties and fuels the rise of divisive populist figures, like Hugo Chávez in Venezuela and Jair Bolsonaro in Brazil.

That finding gave us pause: it showed us that the potential for destructive divisions exists in almost all societies, even ones that seem relatively homogeneous. Our research underscores just how vulnerable democracies are to polarization—and how powerful the factors fueling divisions are.

Partisan conflict takes a heavy toll on civil society as well, often leading to the demonization of activists and human rights defenders. More seriously still, divisions can contribute to a spike in hate crimes and political violence: India, Poland, and the United States have all seen such increases in recent years.

Now is the moment to develop more sustainable security mechanisms in Palestine. The proven practice of unarmed civilian protection and accompaniment is a critical initiative toward such security.

For one, several promising efforts to limit polarization have focused on institutional reforms, such as decentralizing political power or changing electoral rules. Kenya, for instance, adopted a new constitution in 2010 that sought to ease ferocious competition for national office by giving regional officials greater autonomy and control over state resources. But important reforms don’t always require changing a country’s constitution: in the United States, for example, Maine passed legislation in 2016 to enact ranked-choice voting, a system that favors centrist candidates and discourages negative campaigning.

Particularly striking was just how decisive polarizing leaders often are. Figures like Narendra Modi in India, Jarosław Kaczyński in Poland, and Recep Tayyip Erdoğan in Turkey have relentlessly inflamed basic divisions and entrenched them throughout society (often with resounding electoral success). They’ve aggravated tensions not only by demonizing opponents and curtailing democratic processes but also by pushing for radical changes—like a total ban on abortion in Poland.

The degree of similarity we found across countries was startling. Even in democracies as different as Colombia, Kenya, and Poland, many of the roots, patterns, and drivers of polarization were the same.

where s and s' are defined as the object and image distance, respectively. In the case of a spherical lens, the focal length (f) is defined as the image distance for parallel incoming rays:

Polarization tends to escalate at a dizzyingly fast pace, often in the span of just a few years. Just look at how rapidly the 2016 Brexit referendum has ripped the United Kingdom apart.

The focal length f varies with the wavelength of light as illustrated in the tutorial window and Figure 1(a), which demonstrates the effects of chromatic aberration on a beam of white light passing through a simple lens. The component colors (wavelengths) are focused at varying distances from the lens (Figure 2) to produce an image having an arbitrary blur radius approximately 0.3 millimeters in diameter. It is relatively simple to demonstrate chromatic aberration using a thick, simple converging (biconvex, positive meniscus, or plano-convex) lens illuminated with a polychromatic point source, such as a flashlight or candle. When observing an image produced by the simple lens, the periphery of the image will appear blurred and tinted with an orange-red halo when the lens is close to the eye. At greater distances, the halo will become blue-violet.

A final distinctive and perhaps even unique feature of U.S. polarization is the powerful alignment of ethnicity, ideology, and religion on each side of the divide—what we call the “iron triangle” of U.S. polarization. In most other countries, just one or two of those three identity divisions is at the root of polarization; in the United States, all three are. As a result, America’s polarization is unusually encompassing and sharp.

While partisan warfare hasn’t eroded democracy in the United States to the same extent that it has in, say, Bangladesh or Turkey, it is testing our democratic guardrails in serious ways.

The crown/flint combination is termed a lens doublet where each lens has a different refractive index and dispersive properties. Lens doublets are also known as achromatic lenses or achromats for short, derived from the Greek terms a meaning without and chroma meaning color. This simple form of correction allows the image points at 486 nanometers in the blue region and 656 nanometers in the red region to now coincide (Figure 1(b)). Defocus between the central wavelength (550 nanometers) and the common focus (blue and red) is residual aberration that is termed secondary axial color. Even though blur is reduced by a factor of 30 with bichromatic correction using flint and crown glasses (Figure 1(b)), the aberration cannot be completely eliminated with common glass formulations, which limits the image quality of achromatic objectives. Achromats are the most widely used objective lenses and are commonly found on both teaching and research-level laboratory microscopes. Objectives that do not carry a special inscription stating otherwise are likely to be achromats. Achromats are satisfactory objectives for routine laboratory use, but because they are not corrected for all colors, a colorless specimen detail is likely to show, in white light, a pale green color at best focus (secondary axial color).

Linear polarization

These consequences generate a vicious cycle of rising polarization. Attacks on the judiciary, for example, only diminish its capacity to arbitrate conflict and heighten distrust between the opposing sides.

In microscopes having a finite tube length, it is the compensating eyepiece, with chromatic difference of magnification just the opposite of that of the objective, which is utilized to correct for lateral chromatic aberration. Because this defect is also found in higher magnification achromats, compensating eyepieces are frequently used for such objectives, too. Indeed, many manufacturers design their achromats with a standard lateral chromatic error and use compensating eyepieces for all their objectives. Such eyepieces often carry the inscription K or C or Compens. As a result, compensating eyepieces have build-in lateral chromatic error and are not, in themselves, perfectly corrected. In 1976, Nikon introduced CF optics, which correct for lateral chromatic aberration without assistance from the eyepiece. Newer infinity-corrected microscopes either correct chromatic aberration fully in the objective or take advantage of the system objective plus tube lens to render a fully corrected intermediate image.

And while the consequences of polarization are punishing, they don’t necessarily galvanize a government to respond, because the politicians who play the most significant role in exacerbating polarization mostly benefit from it and bear little of the cost.

We focused on nine diverse countries grappling with the problem: Bangladesh, Brazil, Colombia, India, Indonesia, Kenya, Poland, Turkey, and the United States. We assembled a group of scholars with deep local expertise on these countries, and they produced in-depth case studies.

Perhaps most fundamentally, polarization shatters informal but crucial norms of tolerance and moderation—like conceding peacefully after an electoral defeat—that keep political competition within bounds.

Because apochromatic objectives require elements of abnormal dispersion, their characteristics may not be ideal for some specific applications, such as fluorescence excitation in the near ultraviolet, differential interference contrast, and other forms of microscopy utilizing polarized light. For this reason, a fluorite objective is often more suitable, and Figure 4 illustrates how close these objectives are to the performance of apochromats.

Once a society becomes deeply divided, it is very difficult to heal. Before talking about remedial actions, it’s crucial to understand why this problem is so thorny and difficult to overcome.

Chromatic aberration is very common with single thin lenses produced using the classical lens-maker's formula that relates the specimen and image distances for paraxial rays. For a single thin lens fabricated with a material having refractive index n and radii of curvature r(1) and r(2), we can write the following equation:

Polarization examples

Many other drivers of polarization struck us as surprising, even counterintuitive. You might expect, for instance, that a growing economy would ease polarization. Yet we found that in some places, such as India, it actually made things worse. Indeed, the growth of India’s middle class has led to rising support for polarizing Hindu nationalist narratives.

The tutorial initializes with an image of the specimen (as seen through the microscope) appearing in a window on the left-hand side of the applet. Beneath the image window is a pull-down menu labeled Choose A Specimen, which can be used to select a new specimen. The Image Position slider is utilized to control the tutorial by shifting the focal plane along the optical axis of the virtual lens system illustrated as a ray trace pattern on the right-hand side of the applet. The initial position of the slider is the center of the focus range. When the slider is moved to the left, the focal plane is shifted to longer (red) wavelengths and the microscope image and point spread functions simultaneously change to illustrate the effect of chromatic aberration. Moving the slider to the right shifts the focal plane to shorter (blue) wavelengths and produces corresponding changes in the microscope image and point spread functions. A set of radio buttons positioned beneath the ray trace pattern allows the visitor to toggle between an uncorrected virtual optical path and one that has been corrected to simulate achromatic, fluorite, or apochromatic optical elements. Note that clicking on and activating a radio button other than the one labeled Uncorrected will deactivate the Image Position slider.

A lot of research shows how populist and illiberal leaders are putting democracy in danger. But it rarely addresses what we feel is a more fundamental, underlying problem: severe political polarization.

Polarization also reverberates throughout the society as whole, poisoning everyday interactions and relationships. Turkey is a particularly jarring example: almost eight out of ten people there would not want their daughter to marry someone who votes for the party they most dislike. Nearly three-quarters would not even want to do business with such a person.

Polarization in Chemistry

Polarization is shaking societies across the world, from new democracies to long-established ones. Why are political divisions intensifying globally, and what can policymakers learn from other countries’ experiences?

In addition to longitudinal (or axial) chromatic aberration correction, microscope objectives also exhibit another chromatic defect. Even when all three main colors are brought to identical focal planes axially (as in fluorite and apochromat objectives), the point images of details near the periphery of the field of view are not the same size. This occurs because off-axis ray fluxes are dispersed, causing the component wavelengths to form images at different heights on the image plane. For example, the blue image of a detail is slightly larger than the green image or the red image in white light, resulting in color ringing of specimen details at the outer regions of the field of view. Thus, the dependence of axial focal length on wavelength produces a dependence of the transverse magnification on wavelength as well. This defect is known as lateral chromatic aberration or chromatic difference of magnification. When illuminated with white light, a lens with lateral chromatic aberration will produce a series of overlapping images varying in both size and color. In a non-corrected system, the blue component at 436 nanometers may be imaged 1.4 percent larger than the red component at 630 nanometers. Lateral chromatic aberration is greater for objectives of short focal length and can range from 1.1 to 1.9 percent of the radial distance from the optic axis.

The more we looked at the experiences of other divided democracies, the more we realized that U.S. polarization stands out as unusual. It has several distinctive features, and unfortunately, all of them spell trouble for U.S. democracy.

Brian O. Flynn and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.

A comparison of the longitudinal chromatic correction of an achromat with that of an apochromat objective is presented in Figure 3. Glasses of normal dispersion, which have an almost linear decrease in refractive index with increasing wavelength, are used to produce achromat objectives. Only two wavelengths can have the same focus (see Figure 3), and the remaining secondary spectrum produces greenish or purple fringes on images of sharp edges. The higher quality apochromat objectives use glasses having a partial dispersion where the refractive index changes with wavelength more rapidly in either the blue or red region. As a result, apochromats have a high degree of chromatic correction in which up to four wavelengths can have the same image location.

Polarization politics

Chromatic aberrations are wavelength-dependent artifacts that occur because the refractive index of every optical glass formulation varies with wavelength. When white light passes through a simple or complex lens system, the component wavelengths are refracted according to their frequency. In most glasses, the refractive index is greater for shorter (blue) wavelengths and changes at a more rapid rate as the wavelength is decreased.

Lens corrections were first attempted in the latter part of the 18th century when John Dollond, Joseph Lister and Giovanni Amici devised ways to reduce longitudinal chromatic aberration. These pioneers introduced achromatic lenses to microscopy, dramatically reducing axial (longitudinal) chromatic aberration, and made bacteria visible for the first time in the optical microscope. By combining crown glass and flint glass (each type has a different dispersion of refractive index), they succeeded in bringing the blue rays and the red rays to a common focus, near but not identical with the green rays. The dispersion of flint glass is about twice that of crown, so by pairing a positive crown element with a negative flint element, the combined dispersions will be approximately equal and opposite, thus eliminating axial color spread (Figure 2). Note that the magnifying power of the crown glass is twice that of the flint in this combination, yielding a net power about half that of the crown element alone. Another advantage to this lens marriage is the correction for spherical aberration, which often occurs when a positive and negative element are utilized together in a lens group.

Blue light is refracted to the greatest extent followed by green and red light, a phenomenon commonly referred to as dispersion. The inability of a lens to bring all of the colors into a common focus results in a slightly different image size and focal point for each predominant wavelength group. This leads to colored fringes surrounding the image. When the focus is set for the middle of the wavelength band, the image has a green cast with a halo of purple (composed of a mixture of red and blue) surrounding it.

With apochromat and fluorite objectives, the diffraction-induced spreading of the intensity distribution can also be virtually eliminated, as illustrated in Figure 4. An achromat still has substantial intensity in the first fringe, while the apochromat approaches the theoretical resolution limit where the longitudinal chromatic aberration is greater than the wave-optical depth of field.

Polarization in Physics

From these, we extracted cross-cutting findings. And the sheer diversity of our cases—in terms of societal makeup, political institutions, and economic development—opened our eyes to discoveries that we might have missed if we had looked only at the United States and Europe.

Plane of polarization

The Democracy, Conflict, and Governance Program is a leading source of independent policy research, writing, and outreach on global democracy, conflict, and governance. It analyzes and seeks to improve international efforts to reduce democratic backsliding, mitigate conflict and violence, overcome political polarization, promote gender equality, and advance pro-democratic uses of new technologies.

Polarization definition psychology

Other efforts have involved legal or judicial action to limit polarization and majoritarianism—the idea that the feelings and rights of the minority should not constrain leaders with majority support. In India, for example, the Supreme Court has spoken out in defense of democratic institutions and demanded greater accountability for hate crimes and political violence.

Intense partisanship has gripped the United States for an unusually long time and thus become ingrained in social and political life. Today’s divisions date back at least to the 1960s and have been steadily intensifying for over fifty years. Most other current cases of polarization are more recent in origin.

A proper combination of lens thickness, curvature, refractive index, and dispersion allows the doublet to reduce chromatic aberration by bringing two of the wavelength groups into a common focal plane (Figure 2). If fluorspar is introduced into the glass formulation used to fabricate a lens, then the three colors red, green, and blue can be brought into a single focal point resulting in a negligible amount of chromatic aberration. Such lens elements are known as apochromatic lenses and they are used to build very high-quality chromatic aberration-free microscope objectives.

When we looked at the fierce polarization in many countries, we expected to find deep-seated differences between the opposing sides. So we were taken aback to discover that sometimes those differences seem slight.

Our work identifies and analyzes eight different types of remedial actions, ranging from dialogue efforts and media reforms to international action. We’ll highlight just three examples here.

The Democracy, Conflict, and Governance Program is a leading source of independent policy research, writing, and outreach on global democracy, conflict, and governance. It analyzes and seeks to improve international efforts to reduce democratic backsliding, mitigate conflict and violence, overcome political polarization, promote gender equality, and advance pro-democratic uses of new technologies.

In the first place, polarization in the United States isn’t primarily the result of polarizing politicians stoking divisions, as in most other countries. It has deep societal roots and is the outcome of a profound sociocultural struggle between contending conservative and progressive visions of the country. Consequently, U.S. polarization is not something that political leaders can easily reverse, even if they want to.

Yet despite these challenges, our research shows that a wide range of actors have tried inventive ways of addressing the problem—and sometimes achieved encouraging results.

Amplifying the effect of these divisive figures is the technologically fueled disruption of the media industry, especially the rise of social media. Opposition leaders often fan the flames as well by responding with antidemocratic and confrontational tactics of their own. In Turkey, for instance, the head of the main opposition party stoked tensions by calling on the military to oppose Erdoğan’s potential bid for the presidency in 2007.

Polarization of light

It routinely undermines the independence of the judiciary, as politicians attack the courts as biased or pack them with loyalists. It reduces legislatures either to gridlock or to a rubberstamp function. In presidential systems, it frequently leads to the abuse of executive powers and promotes the toxic view that the president represents only his or her supporters, rather than the country as a whole.

Polarization is tearing at the seams of democracies around the world, from Brazil and India to Poland and Turkey. It isn’t just an American illness; it’s a global one.

Polarization then entrenches itself and becomes self-perpetuating. Polarizing actions and reactions feed on each other, dragging countries into a downward spiral of anger and division.

Political leadership can also play a crucial role in de-escalating partisan divides. In Ecuador, President Lenín Moreno has rejected the polarizing tactics of his predecessor, even though the two come from the same political party. And in Turkey, opposition parties have achieved modest success by uniting to form a coalition: their candidate for mayor of Istanbul won a resounding victory in 2019 with a campaign that emphasized overcoming divisions.

Faced with Donald Trump’s return to the White House and his threat to transatlantic relations, the EU is woefully ill-equipped to act swiftly on foreign policy and security issues. An EU Security Council would go a long way in empowering it to respond more effectively.

We wanted to know: Why has polarization come to a boil in so many places in recent years? Are there any telling similarities in the patterns of polarization across different countries? And perhaps most importantly, once societies have become deeply polarized, what can they do to start healing their divisions?

Take the example of Bangladesh: acrimonious political competition there has led to violence, election fraud, and a complete breakdown of democracy. But polarization isn’t rooted in any fundamental ethnic, ideological, or religious division among voters. It is almost entirely the result of power struggles within a political elite that plays up and manufactures divisions.

Modern microscopes utilize this concept, and today it is common to find optical lens triplets made with three lens elements cemented together, especially in higher-quality objectives. For chromatic aberration correction, a typical 10x achromat microscope objective is built with two lens doublets. Many fluorite objectives, which are intermediate in correction between achromats and apochromats, are built using fluorspar (or a similar formulation) combined with an appropriate glass element to form a doublet that is achromatized at three wavelengths. Apochromat objectives usually contain two lens doublets and a lens triplet for advanced correction of both chromatic (up to four wavelengths) and spherical aberrations.

Finally, it is interesting to note that the human eye has a substantial amount of chromatic aberration. Fortunately, we are able to compensate for this artifact when the brain processes images, but it is possible to demonstrate the aberration using a small purple dot on a piece of paper. When held close to the eye, the purple dot will appear blue at the center surrounded by a red halo. As the paper is moved farther away, the dot will appear red surrounded by a blue halo.