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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 \(\theta\). If the electric field has an amplitude \(E\), then the transmitted part of the wave has an amplitude \(E \cos{\theta}\) (Figure \(\PageIndex{7}\)). 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

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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 14. It is apparent that the effect depends on wavelength as well as stress. The wavelength dependence is sometimes also used for artistic purposes.

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All we need to solve these problems are the indices of refraction. Air has \(n_{1} = 100\), water has \(n_{2} = 1.333\), and crown glass has \(n'_{2} = 1.520\). The equation \(\tan{\theta_{b}} = \frac{n_{2}}{n_{1}}\) can be directly applied to find \(\theta_{b}\) in each case.

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Similarly, for crown glass and air, \[\tan{\theta_{b}'} = \frac{n'_{2}}{n_{1}} = \frac{1.520}{1.00} = 1.52.\] Thus, \[\theta_{b}' = \tan{1.52}^{-1} = 56.7^{\circ}.\]

While you are undoubtedly aware of liquid crystal displays (LCDs) found in watches, calculators, computer screens, cellphones, flat screen televisions, and other myriad 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 \(90^{\circ}\). Furthermore, this property can be turned off by the application of a voltage, as illustrated in Figure \(\PageIndex{12}\). 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.

Polaroid sunglasses are familiar to most of us. They have a special ability to cut the glare of light reflected from water or glass (Figure \(\PageIndex{1}\)). Polaroids 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.

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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 \(\PageIndex{13}\)). In addition to depending on the type of substance, the amount and direction of rotation depends on a number of 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 asymmetric 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.

Hence, polarisation is the phenomenon of producing plane polarised light from unpolarised light. In plane polarised light, the plane containing the direction of.

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In flat screen LCD televisions, there is a large light 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 \(\PageIndex{12a}\) and \(\PageIndex{12b}\). 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. One can vary the picture contrast by varying the strength of the voltage applied to the liquid crystal.

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 a angle of reflection \(\theta_{b}\), given by \[\tan{\theta_{b}} = \frac{n_{2}}{n_{1}}, \label{27.9.4}\] where \(n_{1}\) is the medium in which the incident and reflected light travel and \(n_{2}\) 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 \(\theta_{b}\) is known as Brewster's angle, named after the 19th-century Scottish physicist who discovered them.

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Polaroid materials, invented by the founder of 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. Thinking 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 (Figure \(\PageIndex{5}\)).

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If you hold your Polaroid 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 \(\PageIndex{11}\) helps illustrate how this happens. Since light is a transverse EM wave, it vibrates the electrons of air molecules perpendicular to the direction 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 Figure 11, 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 will only be partially polarized. Furthermore, multiple scattering can bring light to your eyes from other directions and can contain different polarizations.

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 not reflected is refracted into these media. So at an incident angle equal to Brewster’s angle, the refracted light will be slightly polarized vertically. It will not be completely polarized vertically, because only a small fraction of the incident light is reflected, and so a significant amount of horizontally polarized light is refracted.

Figure 8 illustrates what happens when unpolarized light is reflected from a surface. Vertically polarized light is preferentially refracted at the surface, so that 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 would be like an arrow perpendicular to the surface and would be more likely to stick and not be reflected. Horizontal polarization is like an arrow bouncing on its side and would be more likely to be reflected. Sunglasses with vertical axes would then block more reflected light than unpolarized light from other sources.

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The Sun and many other light sources produce waves that are randomly polarized (Figure \(\PageIndex{4}\)). Such light is said to be unpolarized because it is composed of many waves with all possible directions of polarization.

Find Polaroid sunglasses and rotate one while holding the other still and look at different surfaces and objects. Explain your observations. What is the difference in angle from when you see a maximum intensity to when you see a minimum intensity? Find a reflective glass surface and do the same. At what angle does the glass need to be oriented to give minimum glare?

There is a range of optical effects used in sunglasses. Besides being Polaroid, other sunglasses have colored pigments embedded in them, while others use non-reflective or even reflective coatings. 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.

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

When the intensity is reduced by \(90.0 \%\), it is \(10.0 \%\) or 0.100 times its original value. That is, \(I = 0.100 I_{0}\). Using this information, the equation \(I = I_{0}\cos{\theta}^{2}\) can be used to solve for the needed angle.

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.

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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 \(45^{\circ}\), the intensity is reduced to \(50\%\) of its original value (as you will show in this section’s Problems & Exercises). Note that \(71.6^{\circ}\) is \(18.4^{\circ}\) from reducing the intensity to zero, and that at an angle of \(18.4^{\circ}\) the intensity is reduced to \(90.0\%\) of its original value (as you will also show in Problems & Exercises), giving evidence of symmetry.

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Polarizing filters have a polarization axis that acts as a slit. This slit passes electromagnetic 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 9.

The LED Ligth Manager (LLM) can drive multiple lights of virtually any type or up to four individual zones or channels within an integrated photometric or multispectral ring light solution. Each program can contain up to six sequences with up to four lights set to continuous on, off, any intensity level in between, and even OverDrive™ strobe mode. To program the four zones of a single LED illumination system such as a ring light or four separate LED light sources, simply connect the LLM to a computer via Ethernet cable and use the browser-based interface to program the light through a series of drop-down menus. The intuitive user interface makes it possible for technicians of any level to set image sequences and program intensities for each light. The LLM system and light kit bundles initially will target 3D photometric stereo and 2D multi-light applications. When used in conjunction with specialized photometric stereo software from Sensopart, the lighting system can solve previously intractable tasks, such as finding a defect in the surface of a part. By capturing successive images of a stationary object as it is illuminated by a sequence of lights, photometric image processing software can determine the 3D surface orientation of every pixel across the object’s surface. The same technique can generate 2D images of multiple regions of interest using separate lights and/or cameras. LLM is also appropriate for multispectral imaging solutions where the LED wavelengths — and not broad-spectrum white lights with optical filters in front of the sensor — are the spectral band selection mechanisms. Using the color of illuminating light as the spectral band selection mechanism can greatly reduce the cost of multispectral imaging solutions, while increasing budgets for imaging applications.

Figure \(\PageIndex{6}\) 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. 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.

Another interesting phenomenon associated with polarized light is the ability of some crystals to split an unpolarized beam of light into two. Such crystals are said to be berefringent (see Figure 15). Each of the separated rays has a specific polarization. One behaves normally and is called the ordinary ray, whereas the other does not obey Snell’s law and is called the extraordinary ray. 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. The interested reader is invited to further pursue the numerous properties of materials related to polarization.

Multi-Zone Ring Lights are designed for compact 3D photometric stereo applications. Compact and powerful, the low-angle mini ring lights work best for dark-field ring applications and radial illumination lighting configurations. Multi-Zone Ring Lights are sold in kits with the 4ZMD Four Channel LED Driver, which permits control of up to four separate lights or light zones, either independently or simultaneously, in any combination and at any intensity level. The 4ZMD strobes the lights independently for photometric and multi-light applications. When connected to SVL’s new programmable LED Light Manager (LLM), each channel of the Multi-Zone Ring lights can be set to continuous on, off, or any intensity level in between, as well as OverDrive™ strobe mode.

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Light is one type of electromagnetic (EM) wave. As noted earlier, EM waves are transverse waves consisting of varying electric and magnetic fields that oscillate perpendicular to the direction of propagation (Figure \(\PageIndex{2}\)). There are specific directions for the oscillations of the electric and magnetic fields. Polarization is the attribute that a wave’s oscillations 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 \(\PageIndex{2}\).

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The Multi-Drive™ controller combines two drives into one with Constant ON operation and OverDrive high-pulse operation. The Multi-Drive™ controller allows the user to run the product in Constant ON operation or pulse/strobe the light at the maximum allowed intensity by simply setting the product parameters. OverDrive operation is five times or more the power vs. constant operation. The built-in Multi-Driver™ also protects the LEDs from premature degradation and failure caused by excessive heat by regulating the current delivered to the LEDs and limiting the duty cycle of the light. Multi-Drive™ offers the best of both worlds. Constant operation can be used with the option of HIGH output strobe/pulse operation. Other advantages of Multi-Drive™ include faster imaging and capture/freeze motion on high-speed lines.

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.

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where \(I_{0}\) is the intensity of the polarized wave before passing through the filter. Equation \ref{27.9.1} is known as Malus’s law.

By now you can probably guess that Polaroid sunglasses cut the glare in reflected light because that light is polarized. You can check this for yourself by holding Polaroid 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.

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Solving the equation \(I = I_{0} \cos{\theta}^{2}\) for \(\cos{\theta}\) and substituting with the relationship between \(I\) and \(I_{0}\) gives

Figure 10 illustrates how the component of the electric field parallel to the long molecules is absorbed. An electromagnetic 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 in the molecules, since electron masses are small. If the electron is forced to oscillate, it can absorb energy from the EM wave. This reduces the fields 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 will allow those fields to pass. Thus the axis of the polarizing filter is perpendicular to the length of the molecule.