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Fun with Surface Tension

There’s a new physicist in our office – a summer intern named Moriel. Over her first few days in the office, Moriel gave us each one of her unique business cards, unique because they include a built-in physics experiment. Impressive. Most impressive. So naturally, we had to try them out…

(SFN members may (did) recognize the subject as one of the forum’s moderators and regular contributors)

That Little Bubble Holds Some Trouble

New Research Result: Bubble Forms Not So Anonymous

How you fill in the bubble has a personal touch.

If bubble marking patterns were completely random, a classifier could do no better than randomly guessing a test set’s creator, with an expected accuracy of 1/92 ≈ 1%. Our classifier achieves over 51% accuracy. The classifier is rarely far off: the correct answer falls in the classifier’s top three guesses 75% of the time (vs. 3% for random guessing) and its top ten guesses more than 92% of the time (vs. 11% for random guessing).

Photography and Physics Tutorial: Filtering and Polarized Light

I ran across this short video on polarizing filters, Polarizing Filters for Photo and Video, and as a very amateur photographer I like tips that help me improve, but as a physicist I was a little dismayed. The presentation is some admixture of being wrong and being incomplete in terms of why the technique works. So I thought I would smooth over the errors and fill in some of the physics gaps.

 

The circular polarizer filter cuts out light coming from only one direction

This is either horribly watered down or misleading or just wrong, depending on your mood. The “light from only one direction” isn’t a reference to the location of the source of the light, it’s a reference to the oscillation direction of the electric field; we can view any source as being a linear combination of some amount of vertically polarized light and horizontally polarized light (or any two perpendicular axes). Unpolarized (or randomly polarized) light will have equal contributions, and polarized light will have more of one than the other; if it’s completely polarized, then it’s all one component.

If you put a linear polarizer in place with 100% linearly polarized light, it will cut down on the light according to Malus’s Law; the intensity varies as \(cos^2theta \) using the angle between the polarizer and the light. But the narrator speaks of a circular polarizer. With circularly polarized light, the direction of the electric field changes as the light travels, so it looks like a helix (wikipedia has an animated gif). If you were looking down the path of the light, it would be a circle. (The general case is that you have the two polarization axes of arbitrary amplitude, and they are out of phase with each other. Then the E field looks like it is mapping out an ellipse, so we call this elliptical polarization).

The tutorial goes through a few examples of using the polarizer to cut down on the glare, along with a reminder that many LCD screens are sources of linearly polarized light. What’s happening in the former case is that reflected light tends to be polarized to some extent, and since that’s sunlight it tends to be bright, so you get glare. To get a good picture, you would like to preferentially reduce the brighter sources, which is why you want to put the polarizer in place as opposed to the neutral density filter, which just makes everything darker. The polarization that takes place on reflection gives you light polarized parallel to the surface, so light reflecting off of a pond or the hood of your car will be horizontally polarized to some extent (this also explains why polarizer sunglasses are useful while driving or at the beach). But light scattering off the atoms in the atmosphere is polarized as well, and that’s a little tougher to figure out, since there’s no “surface” to use as a reference. That’s where a handy tidbit from atomic physics comes in handy: in many ways atoms basically behave like little dipole antennas, and dipoles radiate perpendicular to their axis, but not along their axis. So light from the sun, which is a combination of horizontal and vertical polarization, hits some atom in the atmosphere that’s away from the line between you and the sun. The horizontal polarization looks like its electric field is pointing toward you, and that’s the direction the dipole would want to oscillate — and dipoles don’t radiate along their axis. That polarization is diminished or (at Brewster’s angle) completely gone, which means that the vertical polarization will dominate from the blue sky. Since this does depend on the angle, the filter will have a varying effect, and you can notice this especially with a wide-angle lens.

But all of the talk in the video is about circular polarizers, and as I’ve explained, the light is linearly polarized. A circular polarizer turns linear polarization into circular polarization. So why would it cut down on the amount of linearly polarized light? Here’s what the video isn’t telling you: a circular-polarizer filter for a camera is a linear polarizer and a filter to change the linearly polarized light into circularly polarized light. The linear polarizer does the job of filtering out the linearly polarized light, and then the second component (called a quarter-wave retarder) does its job and gives you the circularly polarized light. Why not just use a linear polarizer and be done with it? Because in any camera where you are seeing light that has come in through the lens (e.g. a typical SLR or video camera, rather than a camera with a separate viewer lens), the light passes through a polarization-dependent beamsplitter that sends half of the light to the viewer and the other half to the meter which tells you how much light there is (and is also important if you use autofocus). But the system expects the light to be unpolarized. If you send it linearly polarized light, there’s an excellent chance the meter will get the wrong amount of light, so the picture will be over- or underexposed (and/or blurry). Circular polarization is the next best thing as far as the meter is concerned, since all polarization directions will be present on the beamsplitter, you still get half the light sent to the meter.

Now that you have some of the physics behind it all, you can go out and use the tips in the video to take some better outdoor pictures.

Star Power Trajectories

Slate‘s Hollywood Career-O-Matic

A visitor to the Rotten Tomatoes site can check out the data for individual Hollywood careers—that’s how Tabarrok came up with the Shyamalan graph—but there’s no easy way for users to measure industrywide trends or to compare different actors and directors side-by-side. To that end, Rotten Tomatoes kindly let Slate analyze the scores in its enormous database and create an interactive tool so our readers might do the same.

It only works from 1985 on, on the hypothesis that people tend not to review old clunkers as often as the classics, which results in sampling bias and this is what skews the older results.

As a general trend, actors seem to be all over the place, score-wise, but directors tend to get better over time.

In this Concave Space, Defined by Orthogonal Dividers, …

Multiplication smackdown: Sal Khan vs Vi Hart—who’s got the ‘insight’?

As usual, Vi delivers a gigantic heaping of insight into what multiplication is, why these algorithms work, along with a handful of sarcasm and one of the most important critiques of math education and obsession with notation I’ve seen in the past month or so.

(New Vi Hart video in the link)

One has to acknowledge that there are different goals in mind for the two videos, but a shortcoming of “turn the crank” cookbook instruction is that you won’t know what to do if you ever encounter a new situation, which is why conveying the deeper understanding is a winner in the long run. Add some enthusiasm for the beauty of math, and that will help foster an interest.

Grad School Gloom and Doom, Part Whatever in a Neverending Series

Faulty Towers: The Crisis in Higher Education

You’re going to be in school for at least seven years, probably more like nine, and there’s a very good chance that you won’t get a job at the end of it.
At Yale, we were overjoyed if half our graduating students found positions. That’s right—half. Imagine running a medical school on that basis. As Christopher Newfield points out in Unmaking the Public University (2008), that’s the kind of unemployment rate you’d expect to find among inner-city high school dropouts.

I’m guessing that if you framed the statistics as doctors who end up working in hospitals you might have a dire employment rate to cite. A fake statistic, but a dramatic one to prove a point. And that’s the problem with most of these “graduate school is broken” articles — the idea that the only career for which you’d go to graduate school is to become a professor. If you aren’t smart enough to realize that a professor churning out more than a few students over the course of his/her career is unsustainable as a closed system, you probably shouldn’t go to grad school. But that’s based on intelligence, not the job market.

That’s not to say that the graduate education system isn’t broken, or at least exploitative, so don’t take away the message that I disagree with the whole article. But let’s be honest in terms of the state of affairs, employment prospects and the goals of graduate school. I think it weakens the argument when you distort the facts. So present some of the real problems, and acknowledge that we’re being misled at some level about what the role of grad school and research is: You can’t simultaneously have a shortage and a glut of scientifically qualified people, and you can’t simultaneously demand (as the article rightly points out) that academia do a lot of research and also not have a lot of grad students around — especially if being a professor requires you spend more time filling out grant applications than doing research. Someone is deceiving us about what’s going on.

Case in point regarding the employment prospects: In FY2009, more than 27,000 H-1B visas were granted to people holding doctorates (pdf alert; a summary exists, too) along with 85,000 Master’s degrees, out of a total of about 214,000 visas. This covers a wider spectrum of occupations than STEM subjects, and unfortunately there is no breakdown of education level correlated to occupation, but if the rough proportion holds then of the tens of thousands of STEM jobs on these visas, about half went to people with graduate degrees of some sort. That’s hard to reconcile with the notion that we have too many graduate students for the economy to absorb. One obvious possible answer is that the system is being abused and we’re importing cheap labor, and I think that’s going on; it’s simply a matter of determining the extent to which it is going on.

But the other issues raised in the article need to be investigated, as well as the solutions. It’s true that the large industrial labs have either evaporated or at least shed their role of basic research, and the government hasn’t stepped in to fill that void. The author also takes on issues of college-level education, which also need solving.