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The light gathering ability of a microscope objective is quantitatively expressed in terms of the numerical aperture (NA). The objective’s NA is a measure of its ability to capture image-forming light rays: Higher NA values allow increasingly oblique rays (representing finer object structures) to enter the front lens of the objective, producing a higher-resolution image with greater specimen detail. This interactive tutorial demonstrates the change in numerical aperture light cones displayed by a microscope objective with corresponding changes in numerical aperture. The angular aperture value corresponding to a given NA-value is also depicted here.
Mr. LaRoche’s sentiment is shared by more and more Americans — that life is less contentious when the people around you vote the way you do.
Mr. Troyer, the Republican from Sioux Falls, moved closer to his wife’s family in Minnesota. Mr. Fisher, the Democrat, moved to escape the harsh South Dakota winters.
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Interviews with 20 recent movers found that, consistent with research on the subject, politics alone did not drive a decision to move. But most we spoke to said it did influence their decision, and for some it topped the must-have list — the movers in our analysis are all registered to vote, and nearly all we spoke to intended to vote on Election Day.
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Our analysis suggests partisanship itself, intentional or not, plays a powerful role when Americans uproot and find a new home. And their very personal decisions about where to resettle help power the churn of migration that is continuously reshaping American life at the neighborhood level and contributing to a sense that Americans are siloed in echo chambers, online and in their daily lives.
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Mr. Troyer, a Republican, on the front porch of his home outside Minneapolis, in a neighborhood that voted for Mr. Trump in 2020 by a wide margin.
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To estimate the difference between Democratic and Republican movers, we leveraged a widely used statistical technique called matching, which enabled us to pair up otherwise similar Democrats and Republicans. We were able to find nearly 750,000 pairs of voters — one Democrat and one Republican each — who were of the same race and gender, who were similar in age and income, and who moved out of the same state and same type of neighborhood.
Previous research has found that most people don’t intentionally seek out politically homogenous areas, but instead share similar preferences with people who vote as they do, with Democrats favoring cities and Republicans favoring the country, on average. A 2015 study, however, found that people favor properties in neighborhoods that reflect their partisan identity.
The most common objectives used on laboratory microscopes are the achromatic objectives. Such objectives are corrected for axial chromatic aberration in blue ...
This is just one pair of voters, but they are part of a trend. Consider the moves of Republicans from relatively balanced neighborhoods like theirs:
High racial diversity means a census tract has a diversity index at the 75th percentile or above. Walkability ratings come from the E.P.A.'s National Walkability Index. Forests include all land classified as a deciduous, evergreen or mixed forest by the US Geological Survey's National Land Cover Database. Neighborhood type definitions are New York Times classifications based on Census data. Temperature data is from the National Centers for Environmental Information. Home value and property tax data from Attom.
“For the most part, you just kind of kept to yourself,” Mr. Fisher, a South Dakota native, said of his old neighborhood, a precinct Mr. Biden won by five points. He says he feels more comfortable in his home in southwest Charlotte, in a precinct Mr. Biden carried by 46 points. “It’s definitely bluer than where we were before, and kind of a nice change,” he said.
Our analysis and interviews suggest just how intertwined political and lifestyle choices can be when it comes to choosing a new home, particularly since 2020.
The 3.5 million movers in our analysis are a small number compared with the 158 million people who voted in 2020, but they do help explain some recent electoral trends — like Florida’s electoral shift to the right or the gains Democrats have made in Georgia.
Mr. Biden won Georgia in 2020, the first time a Democrat won the state since 1992. Among more than 140,000 newcomers, Democrats outnumbered Republicans by more than 9,000. Over the same span, at least 10,000 more Republicans than Democrats moved out of the state — a third of them to Florida.
This is just one pair of voters, but they are part of a trend. Consider the moves of Republicans from relatively balanced neighborhoods like theirs:
In the process, they unwittingly became a part of a nationwide pattern that could matter in a close presidential election.
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Are you curious about how microscope objectives capture finer object structures to produce higher-resolution images? This foundational knowledge article on Numerical Aperture and Light Cone Geometry will give you a sound understanding of the light gathering ability of microscope objectives and how it is expressed through the numerical aperture (NA). An interactive tutorial allows you to visualize changes in the illumination cone as you vary NA values. You will also learn about the role of the refractive index and the limitations of the maximum achievable NA values.
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They have something else in common, too: They both moved away from Sioux Falls. Mr. Troyer left in the fall of 2021, and Mr. Fisher about a year later.
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Ronda Kaysen interviewed several researchers and spoke to 20 recent movers. Ethan Singer analyzed millions of detailed voter registration records.
It’s unclear how much of a direct effect movers might have on the election. Each cycle, the electoral landscape changes in ways that have nothing to do with moving: People turn 18; people die; people change their minds or decide not to vote. But in an extraordinarily close race, even small shifts could prove decisive.
It also has real stakes for our elections: Political scientists say the more partisan a district or state becomes, the less a candidate needs to woo voters from the other party — or, after winning, govern on their behalf.
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Across all movers, Republicans chose neighborhoods Donald J. Trump won by an average of 19 percentage points in 2020, while Democrats chose neighborhoods President Biden won by the opposite margin (also 19 points). In total, movers started in neighborhoods 31 percentage points apart; they ended in neighborhoods 38 points apart. Across the country, the result is a widening gap between blue neighborhoods and red ones.
Erin Thompson, 39, felt out of step as the lone Republican voice among her Seattle friends. Even dating was hard. “You want to find someone who has the same fundamental belief system as you,” she said. Absent that, “It’s just a little isolating.” In 2021, in search of warmer weather and a community more closely matching her worldview, she moved to Gilbert, a conservative Phoenix suburb.
Mr. Troyer, the Republican, moved to a more Republican neighborhood. Mr. Fisher, the Democrat, moved to a more Democratic one.
In Arizona, a state Mr. Biden won by less than 12,000 votes, incoming Republicans — a third of them from California — outnumbered incoming Democrats by a margin of three to two. Accounting for departures, Arizona gained about 17,000 Republican voters.
Theoretically, the maximum angular aperture achievable with a dry (air) microscope objective would be 180 degrees, resulting in a value of 90 degrees for the half angle used in the NA equation. The sine of 90 degrees is one, indicating that the numerical aperture is limited not only by the angular aperture but also by the refractive index of the imaging medium. Most microscope objectives are designed to operate with air (refractive index= 1.0) as the imaging medium between the cover glass and the front lens of the objective. This yields a theoretical maximum NA of 1.00. For practical reasons (available working distance), the highest desirable value for the NA of a dry objective is 0.95 (the half angle of the aperture is approximately 72 degrees). Immersion objectives achieve much higher NAs at the expense of free working distance and spherical aberration sensitivity.
In all but three states that voted for Mr. Biden in 2020, more Democrats have moved in than Republicans. The reverse is true for states Mr. Trump won — in all but one, more Republicans moved in.
object passes is called the objective lens. It should be noted that the light will be inverted at the focal plane. A second lens, referred to as the eyepiece ...
Mr. Fisher, the Democrat, said that while he was eager to escape the snow, he also found the local politics increasingly oppressive. An outspoken liberal, with bumper stickers on his Jeep to match, he was eager to find a place that better reflected his sensibilities.
And yet both ended up in places that were more partisan than where they came from, a phenomenon known as “sorting.” Research on partisanship and migration has found politics typically figures into the equation only indirectly — or even coincidentally.
All movers we spoke to felt politically comfortable in their new homes. Upon retiring, Robert LaRoche, 60, moved from Las Vegas to Spring Hill, Fla., about an hour north of Tampa to live closer to family. While the majority of his old neighbors in a precinct that voted for Mr. Biden by 41 points “did not align with our values,” he said, that’s not why he moved, nor was it why he chose his new home. He sees it as a bonus that he gets to live in a precinct that voted for Mr. Trump in 2020 by 26 points.
Tens of millions of Americans move each year, whether across town or across the country. Most of the voters in our set moved during the pandemic, when home sales surged and many Americans were ready for a change.
Our analysis is an undercount of partisan migration; it may be missing some movers who haven’t yet filed a new address or registered to vote in their new homes. But it probably accounts for most voters who moved, and it shows how population shifts can have political consequences.
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In 36 states, polarization happened in both directions at once: More newcomers were of the winning party, and more of those who left were of the losing party.
“Am I going to fit? Fittingness is a very important criteria for a place to live,” said James Gimpel, a politics professor at the University of Maryland, and co-author of the study. “Nobody wakes up in the morning and says, ‘Gee, I’m looking forward to having a fight with my neighbors.’”
We used party registration data to determine movers’ partisanship in the 30 states where voters can register for a specific party, and used a statistical model based on past vote history and demographics to estimate partisanship in the others. It’s also worth noting that all of the movers we analyzed have, by definition, re-registered to vote some time since 2020. This is important because party registration is a much better indication of partisanship and vote intention for voters who have registered more recently.
Sep 13, 2023 — The ocular lens has three variables: magnification, eye point, and field number. Eyepieces are labeled with key features, similar to objective ...
California has contributed to this trend in a different way: by exporting Republicans en masse. More Republicans have moved out of California than any other state. And those who did have made other states redder in the process — particularly Texas, Arizona, Florida and Nevada.
And Mr. Troyer now lives in Otsego, northwest of Minneapolis, which Mr. Trump won by 27 points. Mr. Troyer said he chose his neighborhood because it was close to his job and family. While he did not intentionally seek out a conservative community, he feels at ease at home and at work. “Everybody I associate with is Republican,” he said. “Everybody at work, the hardworking kind, we’re all Republican.”
The different choices that movers made are not easily explained by things like voters’ ages, race, income or if they were leaving a rural or urban area. Even when narrowing our comparisons to demographically similar pairs of people from the same kinds of neighborhoods — people like Mr. Fisher and Mr. Troyer — Democrats and Republicans still chose neighborhoods that were 24 points apart in the 2020 vote.
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In all three Northern battlegrounds — Pennsylvania, Wisconsin and Michigan — Democrats made small gains through migration. In Pennsylvania, this year’s key battleground, Democratic gains actually came amid population loss: For both parties, more voters moved out than in. But Republicans lost more.
The tutorial displays a schematic drawing of a microscope objective. The actual angular aperture of the light cone and the corresponding NA value are indicated in the tutorial window. To operate the tutorial, use the Numerical Aperture slider to change the NA value from low (left) to high (right). As you vary the numerical aperture value with the slider, the size and shape of the illumination cone entering the objective’s front lens is altered. The adjustable NA for this tutorial is 0.03 to 0.95. The approximate objective magnification has also been assigned to each NA value.
The brightness and resolution of an image formed by an objective at a given magnification increases with its NA value, respectively the diameter of the angular aperture (the angle of the light cone collected by the objective). Light rays emanating from the specimen pass through air (or a liquid-based immersion medium) located between the cover glass and the objective’s front lens. The angular aperture is expressed as the angle between the microscope’s optical axis and the direction of the most oblique light rays captured by the objective (see the tutorial figure). Mathematically, the NA is expressed as:
In 2020, they lived across the street from each other in Sioux Falls, S.D. They are both white men of a similar age. Mr. Fisher, 42, is an auto technician; Mr. Troyer, 39, is a sanitation worker. They are both married. They both have associate degrees.
In contrast, Naomi Hattaway, 48, said politics “did not register one bit” when she moved for work to Fairburn, Ga., a suburb of Atlanta, from Omaha (after a stop in Florida). An independent who previously registered as a Democrat, she said diversity mattered more to her than party affiliation. She feels more at home as a Black mixed race woman in a city with a large Black population and a diverse local government. “It’s everything,” she said, adding that she is “better off living somewhere I belonged.”
Mr. Troyer, the Republican, moved to a more Republican neighborhood. Mr. Fisher, the Democrat, moved to a more Democratic one.
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Romance was also a factor for Andrew Clohessey, 35, who moved to Minneapolis in 2021 from Cedar Falls, Iowa. He’d spent the previous year deliberately applying for jobs in liberal cities, eager to get out of an area that felt increasingly conservative to him, even though his precinct voted for Mr. Biden. He moved into a neighborhood with a lot of shops within walking distance, one that Mr. Biden carried by 61 points. “It’s been great,” he said. On dating apps he is now “more likely to match with people who have left-leaning political views.”
To measure the partisan composition of movers, we relied on nationwide voter registration records provided by the data vendor L2. We used statistical software to match each voter identified by L2 as a mover (based on National Change of Address records) to a 2020 voter registration record in the state that they moved from, allowing us to track movers over time.
n is the refractive index of the media in the object space (between the cover glass and the objective’s front lens) and θ is half the full angular aperture. The value of n varies between 1.0 for air and 1.58 for most immersion media used in optical microscopy. The angular aperture, which varies with the objective focal length, is the maximum angle of image-forming light rays diffracted by the specimen that the front lens of the objective can capture when the specimen is in focus. As the objective focal length decreases, the maximum angle between the specimen and the outer diameter of the objective front lens increases, causing a proportional increase in the angular aperture. From the above equation, it is obvious that the NA increases with both the angular aperture and the refractive index of the imaging medium.
Consider Florida: Once a critical swing state, it has become more reliably Republican. Out of the 3.5 million voters we tracked, more than 200,000 registered Republicans have moved in over the past four years, more than twice the number of Democrats.
Our estimates, based on a New York Times analysis of detailed public voter registration records of more than 3.5 million Americans who moved since the last presidential election, offer a new and extraordinarily detailed glimpse into one of the ways that we segregate from each other — down to the street level.