Only the component of the EM wave parallel to the axis of a filter is passed. Let us call the angle between the direction of polarization and the axis of a filter θ. If the electric field has an amplitude E, then the transmitted part of the wave has an amplitude \(E\cos θ \) (Figure \(\PageIndex{6}\)). Since the intensity of a wave is proportional to its amplitude squared, the intensity I of the transmitted wave is related to the incident wave by

where n1 is the medium in which the incident and reflected light travel and n2 is the index of refraction of the medium that forms the interface that reflects the light. This equation is known as Brewster’s law and θb is known as Brewster’s angle, named after the nineteenth-century Scottish physicist who discovered them.

Figure \(\PageIndex{9}\) illustrates how the component of the electric field parallel to the long molecules is absorbed. An EM wave is composed of oscillating electric and magnetic fields. The electric field is strong compared with the magnetic field and is more effective in exerting force on charges in the molecules. The most affected charged particles are the electrons, since electron masses are small. If an electron is forced to oscillate, it can absorb energy from the EM wave. This reduces the field in the wave and, hence, reduces its intensity. In long molecules, electrons can more easily oscillate parallel to the molecule than in the perpendicular direction. The electrons are bound to the molecule and are more restricted in their movement perpendicular to the molecule. Thus, the electrons can absorb EM waves that have a component of their electric field parallel to the molecule. The electrons are much less responsive to electric fields perpendicular to the molecule and allow these fields to pass. Thus, the axis of the polarizing filter is perpendicular to the length of the molecule.

where \(I_0\) is the intensity of the polarized wave before passing through the filter. This equation is known as Malus’s law.

Many crystals and solutions rotate the plane of polarization of light passing through them. Such substances are said to be optically active. Examples include sugar water, insulin, and collagen (Figure \(\PageIndex{11}\)). In addition to depending on the type of substance, the amount and direction of rotation depend on several other factors. Among these is the concentration of the substance, the distance the light travels through it, and the wavelength of light. Optical activity is due to the asymmetrical shape of molecules in the substance, such as being helical. Measurements of the rotation of polarized light passing through substances can thus be used to measure concentrations, a standard technique for sugars. It can also give information on the shapes of molecules, such as proteins, and factors that affect their shapes, such as temperature and pH.

Some projects are using the XUnit tools to automate regression tests. All of these initiatives are more successful when the test developers have experience building tests. And the next best thing to having experience test automaters on your project (which ClearStream Consulting would be more than happy to supply) is a well-documented set of good test automation practices in the form of patterns.

Automated unit tests (a.k.a. "developer tests") and customer tests (a.k.a. "functional tests") are a cornerstone of many agile development methods (such as eXtreme Programming). The availability of automated, self-checking tests allows developers to be much bolder in how they modify existing software. They allow a more evolutionary form of software development that support incremental delivery of functionality to the customer (motto: Deliver early; deliver often!) that speeds up user feedback and improves the quality (both "fitness for purpose" and "software quality") of the software being built. The techniques are also spreading to less agile development methods via the introduction of "Test Driven Development" as a less extreme process alternative.

Circularpolarization

Since the part of the light that is not reflected is refracted, the amount of polarization depends on the indices of refraction of the media involved. It can be shown that reflected light is completely polarized at an angle of reflection θb given by

Cost effective test automation is all about repeatability, maintainability and communication. Repeatability of results requires repeatability of test fixture setup and repeatability of the interactions with the software under test. And that requires interfaces into the software under test that allow you to put it in the right state before the test and to find out what state it is in after the test. And that can be hard. Throw in the need to make the tests easy to understand and easy to maintain and the problem gets even harder.

The book is organized in 3 major parts. Part I consists of a series of introductory narratives that describe some aspect of test automation using xUnit. This includes a list of Goals and Principles which are summarized on the left size of this diagram:

What is plane polarizedlightin Chemistry

We presented another paper [TAM] at XP/Agile Universe 2003 in New Orleans, Louisiana in which we identified a number of smells and the principles we used to avoid them. These built on papers presented in previous XP conferences on the use of Mock Objects and testing of Frameworks. Discussions with other TDD folk convinced us that there was a real need to share and standardize the vocabulary around XUnit-based test automation. Naturally, patterns were the obvious choice for communicating this knowledge.

All we need to solve these problems are the indices of refraction. Air has n1=1.00, water has n2=1.333, and crown glass has n′2=1.520. The equation \(tan \, θ_b=\frac{n_2}{n_1}\) can be directly applied to find θb in each case.

We started off by writing a paper [IEAT] that we presented at XP2001 in Sardinia, Italy on techniques that we had used to make our tests run much faster. This led to discussions with the inventors of Mock Objects (page X) about whether we were using Mock Objects or some other technique.

Light reflected at these angles could be completely blocked by a good polarizing filter held with its axis vertical. Brewster’s angle for water and air are similar to those for glass and air, so that sunglasses are equally effective for light reflected from either water or glass under similar circumstances. Light that is not reflected is refracted into these media. Therefore, at an incident angle equal to Brewster’s angle, the refracted light is slightly polarized vertically. It is not completely polarized vertically, because only a small fraction of the incident light is reflected, so a significant amount of horizontally polarized light is refracted.

Figure \(\PageIndex{7}\) illustrates what happens when unpolarized light is reflected from a surface. Vertically polarized light is preferentially refracted at the surface, so the reflected light is left more horizontally polarized. The reasons for this phenomenon are beyond the scope of this text, but a convenient mnemonic for remembering this is to imagine the polarization direction to be like an arrow. Vertical polarization is like an arrow perpendicular to the surface and is more likely to stick and not be reflected. Horizontal polarization is like an arrow bouncing on its side and is more likely to be reflected. Sunglasses with vertical axes thus block more reflected light than unpolarized light from other sources.

(a) At what angle will light traveling in air be completely polarized horizontally when reflected from water? (b) From glass?

I am available to provide on-site training at your place of business. If you don't have enough people to justify a dedicated class, I can augment with additional students by listing it as an open enrollment course here and through Agile University. Please feel free to suggest venues where you would like to see a course run. Likewise, please send me your suggestions for future conferences. You can reach me by e-mail using the link at the bottom of each page.

This Open Source Physics animation helps you visualize the electric field vectors as light encounters a polarizing filter. You can rotate the filter—note that the angle displayed is in radians. You can also rotate the animation for 3D visualization.

Polarization of light examplespdf

Polarizing filters have a polarization axis that acts as a slit. This slit passes EM waves (often visible light) that have an electric field parallel to the axis. This is accomplished with long molecules aligned perpendicular to the axis, as shown in Figure \(\PageIndex{8}\).

plane-polarizedlight examples

A range of optical effects are used in sunglasses. Besides being polarizing, sunglasses may have colored pigments embedded in them, whereas others use either a nonreflective or reflective coating. A recent development is photochromic lenses, which darken in the sunlight and become clear indoors. Photochromic lenses are embedded with organic microcrystalline molecules that change their properties when exposed to UV in sunlight, but become clear in artificial lighting with no UV.

Our team has been doing TDD for 6 years since the seminal Kent Beck book. We as a team have learnt read and improved our practice over these years but this book has had the most impact on how 2 do TDD properly. It has significantly improved our code and our testing practices. Many of the leasons we learnt where emphasised and standardised in this book. All I can say is that you will save yourself years and years of hard knocks learning if you read this book first. By following the patterns in this book we have been more easily able to implement the principles in Kent's book. -Brett

The patterns and smells are organized into "categories" that each correspond to a single chapter in the book. The categories are accessible via hyperlinks in the "All Categories" box on the left side. Once a category is selected, the patterns within the category can be accessed from the "All categoryName" box that appears below the "All Categories" box.

Polarization of lightnotes PDF

What angle is needed between the direction of polarized light and the axis of a polarizing filter to reduce its intensity by 90.0%?

Polarized and unpolarizedlight

Solving Malus's law (Equation \ref{Malus's Law}) for \(\cos θ\) and substituting with the relationship between I and I0 gives

By now, you can probably guess that polarizing sunglasses cut the glare in reflected light, because that light is polarized. You can check this for yourself by holding polarizing sunglasses in front of you and rotating them while looking at light reflected from water or glass. As you rotate the sunglasses, you will notice the light gets bright and dim, but not completely black. This implies the reflected light is partially polarized and cannot be completely blocked by a polarizing filter.

The book has won a Jolt Productivity Award in the Best Technical Book category! Here's what the reviewer Rick Wayne said about why the book won the award:

Light is one type of electromagnetic (EM) wave. EM waves are transverse waves consisting of varying electric and magnetic fields that oscillate perpendicular to the direction of propagation (Figure \(\PageIndex{2}\)). However, in general, there are no specific directions for the oscillations of the electric and magnetic fields; they vibrate in any randomly oriented plane perpendicular to the direction of propagation. Polarization is the attribute that a wave’s oscillations do have a definite direction relative to the direction of propagation of the wave. (This is not the same type of polarization as that discussed for the separation of charges.) Waves having such a direction are said to be polarized. For an EM wave, we define the direction of polarization to be the direction parallel to the electric field. Thus, we can think of the electric field arrows as showing the direction of polarization, as in Figure \(\PageIndex{2}\).

Glass and plastic become optically active when stressed: the greater the stress, the greater the effect. Optical stress analysis on complicated shapes can be performed by making plastic models of them and observing them through crossed filters, as seen in Figure \(\PageIndex{12}\). It is apparent that the effect depends on wavelength as well as stress. The wavelength dependence is sometimes also used for artistic purposes.

All the information on this website is organized into categories. The categories are accessible via hyperlinks in the "All Categories" box on the left side. Once a category is selected, the pages (patterns, narratives , etc.) within the category can be accessed from the "All categoryName" box that appears below the "All Categories" box.

The Sun and many other light sources produce waves that have the electric fields in random directions (Figure \(\PageIndex{1a}\)). Such light is said to be unpolarized, because it is composed of many waves with all possible directions of polarization. Polaroid materials—which were invented by the founder of the Polaroid Corporation, Edwin Land—act as a polarizing slit for light, allowing only polarization in one direction to pass through. Polarizing filters are composed of long molecules aligned in one direction. If we think of the molecules as many slits, analogous to those for the oscillating ropes, we can understand why only light with a specific polarization can get through. The axis of a polarizing filter is the direction along which the filter passes the electric field of an EM wave.

If you hold your polarizing sunglasses in front of you and rotate them while looking at blue sky, you will see the sky get bright and dim. This is a clear indication that light scattered by air is partially polarized. Figure \(\PageIndex{10}\) helps illustrate how this happens. Since light is a transverse EM wave, it vibrates the electrons of air molecules perpendicular to the direction that it is traveling. The electrons then radiate like small antennae. Since they are oscillating perpendicular to the direction of the light ray, they produce EM radiation that is polarized perpendicular to the direction of the ray. When viewing the light along a line perpendicular to the original ray, as in the figure, there can be no polarization in the scattered light parallel to the original ray, because that would require the original ray to be a longitudinal wave. Along other directions, a component of the other polarization can be projected along the line of sight, and the scattered light is only partially polarized. Furthermore, multiple scattering can bring light to your eyes from other directions and can contain different polarizations.

Polarizationby reflection

A fairly large angle between the direction of polarization and the filter axis is needed to reduce the intensity to 10.0% of its original value. This seems reasonable based on experimenting with polarizing films. It is interesting that at an angle of 45°, the intensity is reduced to 50% of its original value. Note that 71.6° is 18.4° from reducing the intensity to zero, and that at an angle of 18.4°, the intensity is reduced to 90.0% of its original value, giving evidence of symmetry.

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I've assembled this site to catalog the good practices in xUnit test automation I've encountered over the years. It came about as a result of discussions between me (Gerard Meszaros) and Shaun Smith about the testing techniques we found ourselves using over and over again to solve particular xUnit test automation problems.

Photographs of the sky can be darkened by polarizing filters, a trick used by many photographers to make clouds brighter by contrast. Scattering from other particles, such as smoke or dust, can also polarize light. Detecting polarization in scattered EM waves can be a useful analytical tool in determining the scattering source.

Part II describes a number of "test smells" that are symptoms of problems with how we are automating our tests. These symptoms are summarized in the right side of the previous diagram.

This Open Source Physics animation shows incident, reflected, and refracted light as rays and EM waves. Try rotating the animation for 3D visualization and also change the angle of incidence. Near Brewster’s angle, the reflected light becomes highly polarized.

Examples of polarizationin society

I'll be keeping a brief summary of each pattern & smell on the web site once the book is out. The best place to start is with the Book Outline (or Book Outline Diagrams).

In flat screen LCD televisions, a large light is generated at the back of the TV. The light travels to the front screen through millions of tiny units called pixels (picture elements). One of these is shown in Figure \(\PageIndex{11}\). Each unit has three cells, with red, blue, or green filters, each controlled independently. When the voltage across a liquid crystal is switched off, the liquid crystal passes the light through the particular filter. We can vary the picture contrast by varying the strength of the voltage applied to the liquid crystal.

This page titled 1.8: Polarization is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

To examine this further, consider the transverse waves in the ropes shown in Figure \(\PageIndex{3}\). The oscillations in one rope are in a vertical plane and are said to be vertically polarized. Those in the other rope are in a horizontal plane and are horizontally polarized. If a vertical slit is placed on the first rope, the waves pass through. However, a vertical slit blocks the horizontally polarized waves. For EM waves, the direction of the electric field is analogous to the disturbances on the ropes.

Another interesting phenomenon associated with polarized light is the ability of some crystals to split an unpolarized beam of light into two polarized beams. This occurs because the crystal has one value for the index of refraction of polarized light but a different value for the index of refraction of light polarized in the perpendicular direction, so that each component has its own angle of refraction. Such crystals are said to be birefringent, and, when aligned properly, two perpendicularly polarized beams will emerge from the crystal (Figure \(\PageIndex{14}\)). Birefringent crystals can be used to produce polarized beams from unpolarized light. Some birefringent materials preferentially absorb one of the polarizations. These materials are called dichroic and can produce polarization by this preferential absorption. This is fundamentally how polarizing filters and other polarizers work.

I have been reading the various conference papers and (mostly JUnit-based) books on test automation for quite some time. Each author seems to have a particular area of interest and favorite techniques. While I don't always agree with their practices, I am always trying to understand why they do it a particular way and *when* it would be more appropriate to use their techniques than the ones I already use.

Although we did not specify the direction in Example \(\PageIndex{1}\), let’s say the polarizing filter was rotated clockwise by 71.6° to reduce the light intensity by 90.0%. What would be the intensity reduction if the polarizing filter were rotated counterclockwise by 71.6°?

When the intensity is reduced by 90.0%, it is 10.0% or 0.100 times its original value. That is, I=0.100I0. Using this information, the equation I=I0cos2θ can be used to solve for the needed angle.

The major boxes in each of the preceding diagrams corresponds to a chapter in the corresponding part of the book; they also correspond the "categories" listed in the top left navigation sidebar on this web site. Selecting a category provides a list of patterns or smells in the category and selecting a specific pattern or smell adds a list of aliases, causes and variations of the chosen pattern or smell.

Figure \(\PageIndex{5}\) shows the effect of two polarizing filters on originally unpolarized light. The first filter polarizes the light along its axis. When the axes of the first and second filters are aligned (parallel), then all of the polarized light passed by the first filter is also passed by the second filter. If the second polarizing filter is rotated, only the component of the light parallel to the second filter’s axis is passed. When the axes are perpendicular, no light is passed by the second filter.

Unit testing is hardly news, but simply writing a ton of tests guarantees you no bliss. Gerard Meszaros's xUnit Test Patterns distills and codifies the crucial meta-knowledge to take us to the next level. Why do good tests go bad, and how do you fix them--it's as simple and groundbreaking as that. Smells and antipatterns arise in tests that cripple their maintainability. xUnit Test Patterns exhaustively describes those pathologies and provides the prescription in the catalog format familiar since 1994. But fear not - every motivation and pattern includes at least one source-code example and the explanations are couched in clear, direct language. If you're ready to promote your test code to the same level of care and craftsmanship that you devote to production systems, grab a copy of xUnit Test Patterns and get cracking.

Of course, you can access the material in "book order" by starting in Book Outline. Because so much has changed during the copy editing process, I'll be "abridging" the material on this web site once the book is out. I will, however, keep a brief summary of each pattern & smell on the site as well as many of the cross reference tables.

Automated tests take a lot less effort to run than manual tests. As a result, they are more likely to be run often. The more often the better. Fully assimilated agile developers run their tests pretty well every time they save and compile their code. And any time they need a quick vote of confidence! The tests act as a comforting "safety net" that promises to catch the developer's mistakes. This allows them to work more quickly and with less paranoia and that makes them more productive despite the extra effort involved in writing the tests.

All patterns, smells, etc. are first introduced in a series of narratives that provide an overview of a particular topic area. The narratives are accessible via the special category "Narratives" from the "All Categories" box or from the Book Outline.

Part III contains descriptions of the patterns. The chapters correspond to the major boxes in the following diagram:

Although you are undoubtedly aware of liquid crystal displays (LCDs) found in watches, calculators, computer screens, cellphones, flat screen televisions, and many other places, you may not be aware that they are based on polarization. Liquid crystals are so named because their molecules can be aligned even though they are in a liquid. Liquid crystals have the property that they can rotate the polarization of light passing through them by 90°. Furthermore, this property can be turned off by the application of a voltage, as illustrated in Figure \(\PageIndex{11}\). It is possible to manipulate this characteristic quickly and in small, well-defined regions to create the contrast patterns we see in so many LCD devices.

The book is now available at retailers and sample chapters are available for download from Addison Wesley Professional's website. It is available in both traditional print form through most booksellers and as a PDF e-book (but only from the AW website.) Note that the material here is now somewhat out of step with the book content because it hasn't been updated based on the results of copy editing.

This is one of the major different between prose that merely explains a technique and a pattern. Patterns help the reader understand the WHY behind each practice so they can make intelligent choices between the alternative patterns (and thereby avoid nasty consequences from surprising them later.)

Polarizing sunglasses are familiar to most of us. They have a special ability to cut the glare of light reflected from water or glass (Figure \(\PageIndex{1}\)). They have this ability because of a wave characteristic of light called polarization. What is polarization? How is it produced? What are some of its uses? The answers to these questions are related to the wave character of light.

Automated test are more repeatable than manual tests because they execute exactly the same way every time. They don't forget things after long weekends and vacations. They don't leave to work on other projects. They don't get sick or run over by a bus.

Since XP/Agile Universe 2003, we have been cataloging all the patterns we regularly use and the obvious alternatives that we have consciously chosen not to use. We have also been looking through the mostly JUnit-based books on test automation to see what others are advocating looking for techniques whether or not they are described as patterns. There is some obvious overlap between the various material but also seem to be considerable gaps and no comprehensive treatment of the topic. As of October 2003, we had identified over 120 patterns ranging from principles and strategies to coding-level idioms!

Automating tests using XUnit is a form of software whether you write the tests before or after the code it tests. But the goals of this test software ("testware") is very different from the software most people are used to writing. Writing it is optional so we can stop writing it or maintaining it at any time. So we need compelling reason to (keep) writing them. And there is a lot to think about when automating tests. How do I interact with the SUT? What is the best way to express the expected outcome? How can I keep tests from breaking each other? How can I ensure the tests will work next week, next month, even next year? How do I test when the software under test depends on software that hasn't been written yet? Or cannot be used in our test environment? Or makes the tests take too long to run? If writing the tests is hard and has little benefit, we just won't do it any more!