When red light passes through a green filter, no light gets through. What happens to it?

Learning Objectives

By the end of this section, you will exist able

• Discuss the significant of polarization.
• Discuss the belongings of optical activity of certain materials.

Polaroid sunglasses are familiar to most of united states. They have a special power to cut the glare of light reflected from water or glass (run across Figure 1). Polaroids have this ability because of a moving ridge characteristic of light called polarization. What is polarization? How is information technology produced? What are some of its uses? The answers to these questions are related to the moving ridge graphic symbol of light.

Figure 1. These two photographs of a river show the effect of a polarizing filter in reducing glare in light reflected from the surface of h2o. Part (b) of this Figure was taken with a polarizing filter and office (a) was non. As a result, the reflection of clouds and heaven observed in function (a) is not observed in part (b). Polarizing sunglasses are particularly useful on snow and water. (credit: Amithshs, Wikimedia Commons)

Figure ii. An EM wave, such as calorie-free, is a transverse wave. The electric and magnetic fields are perpendicular to the direction of propagation.

Light is one blazon 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 (see Figure 2). In that location are specific directions for the oscillations of the electric and magnetic fields. Polarization is the aspect that a moving ridge'southward oscillations have a definite direction relative to the management of propagation of the wave. (This is not the same type of polarization every bit 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 nosotros tin can think of the electric field arrows as showing the direction of polarization, as in Figure 2.

To examine this further, consider the transverse waves in the ropes shown in Figure 3. The oscillations in ane 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 kickoff rope, the waves pass through. Even so, 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.

Effigy three. The transverse oscillations in ane rope are in a vertical plane, and those in the other rope are in a horizontal plane. The first is said to be vertically polarized, and the other is said to be horizontally polarized. Vertical slits pass vertically polarized waves and block horizontally polarized waves.

Figure 4. The slender arrow represents a ray of unpolarized lite. The bold arrows represent the direction of polarization of the individual waves composing the ray. Since the calorie-free is unpolarized, the arrows point in all directions.

The Sun and many other light sources produce waves that are randomly polarized (see Effigy 4). Such low-cal is said to be unpolarized because it is composed of many waves with all possible directions of polarization. Polaroid materials, invented by the founder of Polaroid Corporation, Edwin Land, act as a polarizing slit for light, assuasive only polarization in i direction to laissez passer through. Polarizing filters are equanimous of long molecules aligned in i management. Thinking of the molecules as many slits, coordinating to those for the oscillating ropes, nosotros can understand why only lite with a specific polarization can get through. The axis of a polarizing filter is the direction along which the filter passes the electrical field of an EM wave (run into Figure 5).

Figure 5. A polarizing filter has a polarization axis that acts as a slit passing through electrical fields parallel to its direction. The management of polarization of an EM moving ridge is defined to be the direction of its electric field.

Figure 6 shows the result of two polarizing filters on originally unpolarized light. The first filter polarizes the calorie-free along its centrality. When the axes of the first and 2d filters are aligned (parallel), then all of the polarized light passed by the starting time filter is also passed by the second. If the second polarizing filter is rotated, only the component of the calorie-free parallel to the second filter'southward axis is passed. When the axes are perpendicular, no light is passed by the second.

Figure 6. The upshot of rotating ii polarizing filters, where the first polarizes the light. (a) All of the polarized light is passed past the 2nd polarizing filter, because its axis is parallel to the first. (b) As the second is rotated, simply part of the light is passed. (c) When the second is perpendicular to the showtime, no lite is passed. (d) In this photograph, a polarizing filter is placed above two others. Its axis is perpendicular to the filter on the correct (night area) and parallel to the filter on the left (lighter surface area). (credit: P.P. Urone)

Figure 7. A polarizing filter transmits only the component of the moving ridge parallel to its centrality, , reducing the intensity of whatsoever light not polarized parallel to its centrality.

Only the component of the EM wave parallel to the axis of a filter is passed. Permit united states telephone 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 cosθ (see Effigy 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 byI =I ₀ cos²θ,where I ₀ is the intensity of the polarized wave earlier passing through the filter. (The above equation is known equally Malus's constabulary.)

Case 1. Calculating Intensity Reduction by a Polarizing Filter

What angle is needed between the management of polarized low-cal and the axis of a polarizing filter to reduce its intensity by 90.0%?

Strategy

When the intensity is reduced by 90.0%, it is 10.0% or 0.100 times its original value. That is, I= 0.100I ₀. Using this information, the equationI =I ₀ cos²θ can exist used to solve for the needed angle.

Solution

Solving the equationI =I ₀ cos^twoθ for cosθ and substituting with the relationship between I and I ₀ gives

[latex]\displaystyle\cos\theta=\sqrt{\frac{I}{I_0}}=\sqrt{\frac{0.100 I_0}{I_0}}=0.3162\\[/latex]

Solving for θ yieldsθ = cos⁻¹ 0.3162 = 71.6º.

Discussion

A adequately large angle between the direction of polarization and the filter centrality 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 45º, the intensity is reduced to 50% of its original value (every bit you lot will bear witness in this section's Problems & Exercises). Note that 71.6º is 18.4º from reducing the intensity to zippo, and that at an angle of xviii.4º the intensity is reduced to 90.0% of its original value (as you volition also show in Problems & Exercises), giving testify of symmetry.

Polarization by Reflection

By now you can probably guess that Polaroid sunglasses cut the glare in reflected calorie-free because that light is polarized. You tin can bank check this for yourself by belongings Polaroid sunglasses in front of y'all and rotating them while looking at light reflected from water or glass. As you rotate the sunglasses, you lot will find the light gets brilliant and dim, but not completely black. This implies the reflected light is partially polarized and cannot exist completely blocked by a polarizing filter.

Figure 8. Polarization by reflection. Unpolarized light has equal amounts of vertical and horizontal polarization. After interaction with a surface, the vertical components are preferentially captivated or refracted, leaving the reflected light more horizontally polarized. This is akin to arrows striking on their sides bouncing off, whereas arrows striking on their tips get into the surface.

Figure 8 illustrates what happens when unpolarized light is reflected from a surface. Vertically polarized low-cal is preferentially refracted at the surface, so that the reflected lite is left more horizontally polarized. The reasons for this phenomenon are across the scope of this text, but a convenient mnemonic for remembering this is to imagine the polarization management to be like an arrow. Vertical polarization would be similar an arrow perpendicular to the surface and would be more than likely to stick and not exist reflected. Horizontal polarization is like an arrow billowy on its side and would be more likely to be reflected. Sunglasses with vertical axes would and then cake more reflected light than unpolarized light from other sources.

Since the part of the light that is not reflected is refracted, the corporeality of polarization depends on the indices of refraction of the media involved. It can be shown that reflected light is completely polarized at a bending of reflection θ _b, given by [latex]\tan\theta_{\text{b}}=\frac{n_2}{n_1}\\[/latex], where n _i 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 every bit Brewster's law, and θ _b is known as Brewster's angle, named later the 19th-century Scottish physicist who discovered them.

Things Great and Pocket-size: Diminutive Caption of Polarizing Filters

Polarizing filters have a polarization axis that acts as a slit. This slit passes electromagnetic waves (often visible calorie-free) that have an electric field parallel to the centrality. This is accomplished with long molecules aligned perpendicular to the axis equally shown in Figure nine.

Figure 9. Long molecules are aligned perpendicular to the centrality of a polarizing filter. The component of the electric field in an EM wave perpendicular to these molecules passes through the filter, while the component parallel to the molecules is absorbed.

Figure x illustrates how the component of the electrical field parallel to the long molecules is absorbed. An electromagnetic wave is composed of oscillating electric and magnetic fields. The electrical 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 free energy from the EM wave. This reduces the fields in the wave and, hence, reduces its intensity. In long molecules, electrons tin more easily oscillate parallel to the molecule than in the perpendicular direction. The electrons are jump to the molecule and are more restricted in their movement perpendicular to the molecule. Thus, the electrons tin 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 volition allow those fields to pass. Thus the axis of the polarizing filter is perpendicular to the length of the molecule.

Figure 10. Artist's conception of an electron in a long molecule oscillating parallel to the molecule. The oscillation of the electron absorbs energy and reduces the intensity of the component of the EM moving ridge that is parallel to the molecule.

Example 2. Calculating Polarization by Reflection

1. At what angle will light traveling in air be completely polarized horizontally when reflected from water?
2. From glass?

Strategy

All nosotros need to solve these problems are the indices of refraction. Air has n ₁ = i.00, water has n ₂ = one.333, and crown glass has n′₂=1.520. The equation [latex]\tan\theta_{\text{b}}=\frac{n_2}{n_1}\\[/latex] can be straight applied to notice θ _b in each instance.

Solution for Part 1

Putting the known quantities into the equation

[latex]\tan\theta_{\text{b}}=\frac{n_2}{n_1}\\[/latex] gives [latex]\tan\theta_{\text{b}}=\frac{n_2}{n_1}=\frac{1.333}{ane.00}=1.333\\[/latex].

Solving for the angle θ _b yields

θ _b = tan⁻¹ ane.333 = 53.1º.

Solution for Role 2

Similarly, for crown glass and air,

[latex]\tan\theta^{\prime}_{\text{b}}=\frac{n^{\prime number}_2}{n_1}=\frac{1.520}{ane.00}=1.52\\[/latex].

Thus,

θ′ _b = tan⁻ⁱ i.52 = 56.7º.

Discussion

Light reflected at these angles could exist completely blocked past a good polarizing filter held with its centrality vertical. Brewster's angle for h2o and air are similar to those for glass and air, so that sunglasses are equally effective for light reflected from either h2o or glass under similar circumstances. Low-cal not reflected is refracted into these media. So at an incident angle equal to Brewster's angle, the refracted lite will exist slightly polarized vertically. Information technology will non exist completely polarized vertically, because simply a small fraction of the incident lite is reflected, then a significant amount of horizontally polarized calorie-free is refracted.

Polarization past Scattering

Effigy 11. Polarization by scattering. Unpolarized light handful from air molecules shakes their electrons perpendicular to the management of the original ray. The scattered light therefore has a polarization perpendicular to the original direction and none parallel to the original direction.

If you hold your Polaroid sunglasses in front of yous and rotate them while looking at blue sky, you volition see the sky get bright and dim. This is a clear indication that light scattered by air is partially polarized. Figure 11 helps illustrate how this happens. Since light is a transverse EM moving ridge, it vibrates the electrons of air molecules perpendicular to the direction information technology is traveling. The electrons then radiate similar modest antennae. Since they are aquiver 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 tin can be no polarization in the scattered light parallel to the original ray, considering that would require the original ray to be a longitudinal wave. Forth other directions, a component of the other polarization tin can be projected along the line of sight, and the scattered calorie-free will only be partially polarized. Furthermore, multiple scattering can bring light to your eyes from other directions and can contain dissimilar polarizations.

Photographs of the sky tin can be darkened by polarizing filters, a fob used by many photographers to make clouds brighter by contrast. Scattering from other particles, such every bit fume or dust, can also polarize low-cal. Detecting polarization in scattered EM waves tin can be a useful analytical tool in determining the handful source.

There is a range of optical effects used in sunglasses. Too being Polaroid, other sunglasses have colored pigments embedded in them, while others utilize not-reflective or fifty-fifty reflective coatings. A recent development is photochromic lenses, which darken in the sunlight and get articulate indoors. Photochromic lenses are embedded with organic microcrystalline molecules that alter their properties when exposed to UV in sunlight, simply become clear in bogus lighting with no UV.

Have-Home Experiment: 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 lot run into a maximum intensity to when you encounter a minimum intensity? Find a reflective drinking glass surface and do the aforementioned. At what angle does the drinking glass need to be oriented to requite minimum glare?

Liquid Crystals and Other Polarization Furnishings in Materials

While you are undoubtedly enlightened of liquid crystal displays (LCDs) found in watches, calculators, figurer 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 holding that they can rotate the polarization of low-cal passing through them by 90º. Furthermore, this belongings tin can be turned off by the application of a voltage, every bit illustrated in Figure 12. Information technology is possible to dispense this characteristic quickly and in small well-defined regions to create the dissimilarity patterns we see in and so many LCD devices.

In flat screen LCD televisions, there is a large light at the dorsum of the TV. The light travels to the forepart screen through millions of tiny units called pixels (flick elements). Ane of these is shown in Figure 12 (a) and (b). Each unit of measurement has three cells, with red, blue, or light-green filters, each controlled independently. When the voltage across a liquid crystal is switched off, the liquid crystal passes the light through the item filter. One can vary the picture contrast by varying the forcefulness of the voltage applied to the liquid crystal.

Figure 12. (a) Polarized light is rotated 90º by a liquid crystal and then passed by a polarizing filter that has its axis perpendicular to the original polarization direction. (b) When a voltage is practical to the liquid crystal, the polarized lite is not rotated and is blocked by the filter, making the region night in comparison with its surroundings. (c) LCDs can be made color specific, small-scale, and fast enough to utilize in laptop computers and TVs. (credit: Jon Sullivan)

Many crystals and solutions rotate the plane of polarization of calorie-free passing through them. Such substances are said to exist optically active. Examples include sugar water, insulin, and collagen (see Figure 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 activeness is due to the disproportionate shape of molecules in the substance, such as existence helical. Measurements of the rotation of polarized light passing through substances can thus be used to mensurate concentrations, a standard technique for sugars. Information technology can also give information on the shapes of molecules, such every bit proteins, and factors that affect their shapes, such as temperature and pH.

Figure 13. Optical activity is the ability of some substances to rotate the plane of polarization of light passing through them. The rotation is detected with a polarizing filter or analyzer.

Glass and plastic become optically agile when stressed; the greater the stress, the greater the issue. Optical stress assay on complicated shapes can exist performed by making plastic models of them and observing them through crossed filters, equally seen in Effigy xiv. It is credible that the effect depends on wavelength also as stress. The wavelength dependence is sometimes also used for artistic purposes.

Figure 14. Optical stress assay of a plastic lens placed betwixt crossed polarizers. (credit: Infopro, Wikimedia Commons)

Some other interesting phenomenon associated with polarized low-cal is the ability of some crystals to split an unpolarized axle of calorie-free into two. Such crystals are said to be birefringent (see Figure 15). Each of the separated rays has a specific polarization. One behaves unremarkably and is called the ordinary ray, whereas the other does not obey Snell'due south 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 tin produce polarization past this preferential absorption. This is fundamentally how polarizing filters and other polarizers work. The interested reader is invited to further pursue the numerous backdrop of materials related to polarization.

Figure xv. Birefringent materials, such as the common mineral calcite, separate unpolarized beams of light into two. The ordinary ray behaves every bit expected, but the boggling ray does not obey Snell'south law.

Department Summary

• Polarization is the attribute that wave oscillations take a definite management relative to the direction of propagation of the wave.
• EM waves are transverse waves that may be polarized.
• The direction of polarization is defined to be the direction parallel to the electric field of the EM wave.
• Unpolarized lite is composed of many rays having random polarization directions.
• Light can be polarized by passing information technology through a polarizing filter or other polarizing cloth. The intensity I of polarized light subsequently passing through a polarizing filter is I = I ₀ cos^twoθ, where I₀ is the original intensity and θ is the bending betwixt the direction of polarization and the axis of the filter.
• Polarization is also produced by reflection.
• Brewster'southward law states that reflected calorie-free will be completely polarized at the angle of reflection θ _b, known as Brewster's angle, given by a statement known as Brewster'southward police: [latex]\tan{\theta }_{\text{b}}=\frac{{n}_{ii}}{{north}_{1}}\\[/latex], where n ₁ is the medium in which the incident and reflected light travel and n ₂ is the alphabetize of refraction of the medium that forms the interface that reflects the lite.
• Polarization can also exist produced by scattering.
• There are a number of types of optically active substances that rotate the direction of polarization of light passing through them.

Conceptual Questions

1. Under what circumstances is the phase of light changed by reflection? Is the phase related to polarization?
2. Tin a sound wave in air be polarized? Explain.
3. No light passes through two perfect polarizing filters with perpendicular axes. However, if a tertiary polarizing filter is placed between the original two, some light can laissez passer. Why is this? Nether what circumstances does nigh of the lite pass?
4. Explain what happens to the energy carried by light that information technology is dimmed by passing it through two crossed polarizing filters.
5. When particles scattering low-cal are much smaller than its wavelength, the corporeality of handful is proportional to [latex]\frac{1}{{\lambda }^{4}}\\[/latex]. Does this mean there is more scattering for modest λ than large λ? How does this relate to the fact that the sky is blue?
6. Using the data given in the preceding question, explain why sunsets are reddish.
7. When light is reflected at Brewster's angle from a smooth surface, it is 100% polarized parallel to the surface. Part of the light will be refracted into the surface. Describe how you would do an experiment to make up one's mind the polarization of the refracted light. What management would yous expect the polarization to have and would y'all wait it to be 100%?

Problems & Exercises

1. What bending is needed betwixt the direction of polarized light and the axis of a polarizing filter to cut its intensity in half?
2. The bending betwixt the axes of ii polarizing filters is 45.0º. Past how much does the second filter reduce the intensity of the light coming through the first?
3. If you accept completely polarized light of intensity 150 W/1000^two, what volition its intensity be later passing through a polarizing filter with its axis at an 89.0º bending to the lite'due south polarization direction?
4. What angle would the axis of a polarizing filter need to make with the direction of polarized low-cal of intensity one.00 kW/1000^two to reduce the intensity to 10.0 W/1000^two?
5. At the stop of Example 1, information technology was stated that the intensity of polarized light is reduced to 90.0% of its original value by passing through a polarizing filter with its axis at an bending of eighteen.4º to the direction of polarization. Verify this argument.
6. Bear witness that if you have three polarizing filters, with the second at an angle of 45º to the starting time and the tertiary at an angle of ninety.0º to the kickoff, the intensity of light passed by the kickoff will be reduced to 25.0% of its value. (This is in dissimilarity to having simply the first and third, which reduces the intensity to zero, so that placing the 2nd between them increases the intensity of the transmitted light.)
7. Prove that, if I is the intensity of light transmitted past two polarizing filters with axes at an angle θ and I′ is the intensity when the axes are at an angle 90.0º −θ, then I+ I ′ = I ₀ the original intensity. (Hint: Apply the trigonometric identities cos (xc.0º −θ) = sinθ and cosⁱⁱθ + sin²θ = 1.)
8. At what angle will light reflected from diamond be completely polarized?
9. What is Brewster'due south bending for light traveling in water that is reflected from crown glass?
10. A scuba diver sees light reflected from the water'south surface. At what angle will this light be completely polarized?
11. At what angle is light inside crown glass completely polarized when reflected from h2o, as in a fish tank?
12. Light reflected at 55.6º from a window is completely polarized. What is the window'due south index of refraction and the likely substance of which it is made?
13. (a) Light reflected at 62.5º from a gemstone in a band is completely polarized. Tin the precious stone be a diamond? (b) At what angle would the light be completely polarized if the gem was in h2o?
14. If θ _b is Brewster's angle for lite reflected from the pinnacle of an interface between ii substances, and θ′_b is Brewster'southward angle for light reflected from beneath, prove thatθ _b+θ′_b = 90.0º.
15. Integrated Concepts. If a polarizing filter reduces the intensity of polarized low-cal to 50.0% of its original value, past how much are the electric and magnetic fields reduced?
16. Integrated Concepts. Suppose you put on ii pairs of Polaroid sunglasses with their axes at an angle of 15.0º. How much longer will it take the lite to eolith a given amount of energy in your eye compared with a single pair of sunglasses? Presume the lenses are clear except for their polarizing characteristics.
17. Integrated Concepts. (a) On a day when the intensity of sunlight is 1.00 kW/grand^two, a circular lens 0.200 yard in diameter focuses light onto water in a black chalice. 2 polarizing sheets of plastic are placed in front of the lens with their axes at an bending of 20.0º. Assuming the sunlight is unpolarized and the polarizers are 100% efficient, what is the initial charge per unit of heating of the water in ºC/s, assuming it is fourscore.0% absorbed? The aluminum beaker has a mass of xxx.0 grams and contains 250 grams of h2o. (b) Do the polarizing filters get hot? Explain.

Glossary

axis of a polarizing filter: the management along which the filter passes the electric field of an EM wave

birefringent: crystals that divide an unpolarized beam of light into 2 beams

Brewster's angle: [latex]{\theta }_{\text{b}}={\tan}^{-1}\left(\frac{{n}_{2}}{{n}_{ane}}\right)\\[/latex], where n _ii is the index of refraction of the medium from which the calorie-free is reflected and due north _one is the alphabetize of refraction of the medium in which the reflected calorie-free travels

Brewster's law: [latex]\tan\theta_{\text{b}}=\frac{{due north}_{2}}{{north}_{1}}\\[/latex], wheren _i 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

direction of polarization: the direction parallel to the electric field for EM waves

horizontally polarized: the oscillations are in a horizontal plane

optically active: substances that rotate the aeroplane of polarization of light passing through them

polarization: the attribute that wave oscillations have a definite direction relative to the direction of propagation of the wave

polarized: waves having the electric and magnetic field oscillations in a definite management

reflected light that is completely polarized: light reflected at the bending of reflection θ _b, known equally Brewster's angle

unpolarized: waves that are randomly polarized

vertically polarized: the oscillations are in a vertical plane

Selected Solutions to Problems & Exercises

1. 45.0º

3. 45.vii mW/chiliad²

5. 90.0%

7.I ₀

ix. 48.8º

xi. 41.2º

13. (a) 1.92, not diamond (Zircon); (b) 55.2º

fifteen.B _two = 0.707B ₁

17. (a) 2.07 × x⁻² °C/s; (b) Aye, the polarizing filters get hot considering they absorb some of the lost energy from the sunlight.

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Source: https://courses.lumenlearning.com/physics/chapter/27-8-polarization/

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