What Is The Angle Between The Electric Field And The Axis Of The Filter?

Chapter 12 – Wave Eyes

12.viii Polarization

Summary

Talk over the meaning of polarization.
Discuss the belongings of optical activeness of sure materials.

Polaroid sunglasses are familiar to nearly of united states. They take a special ability to cutting the glare of light reflected from water or glass as shown in the effigy beneath. Polaroids have this ability considering of a wave 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 wave grapheme of light.

Two photographs side by side of the same calm stream bed. In photograph a, the reflections of the clouds and some blue sky prevent you from seeing the pebbles in the streambed. In photograph b, there is essentially no reflection of the sky from the water's surface, and the pebbles underneath the water are clearly visible. — **Figure ane.** These two photographs of a river show the effect of a polarizing filter in reducing glare in light reflected from the surface of water. Part (b) of this effigy was taken with a polarizing filter and part (a) was non. As a result, the reflection of clouds and sky observed in function (a) is not observed in part (b). Polarizing sunglasses are especially useful on snowfall and water. (credit: Amithshs, Wikimedia Commons)

Calorie-free is one type of electromagnetic (EM) wave. Every bit noted earlier, EM waves are transverse waves consisting of varying electric and magnetic fields that oscillate perpendicular to the management of propagation (see Effigy ii). In that location are specific directions for the oscillations of the electrical and magnetic fields. Polarization is the attribute that a moving ridge'southward oscillations take a definite direction relative to the direction of propagation of the wave. (This is not the aforementioned type of polarization as that discussed for the separation of charges.) Waves having such a management 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 tin think of the electric field arrows equally showing the direction of polarization, every bit in Figure 2.

The schematic shows an axis labeled c that points to the right. On this axis are two sinusoidal waves that are in phase. The wave labeled E oscillates up down in the vertical plane and the wave labeled B oscillates back and forth in the horizontal plane. At the tip of the axis c is a double headed arrow oriented vertically that is labeled direction of polarization. — **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.

To examine this further, consider the transverse waves in the ropes shown in Figure three. The oscillations in one rope are in a vertical plane and are said to exist vertically polarized. Those in the other rope are in a horizontal plane and are horizontally polarized. If a vertical slit is placed on the commencement rope, the waves laissez passer 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.

The figure shows waves on a vertically oscillating rope that pass through a vertical slit. A separate drawing shows waves on a horizontally oscillating rope that do not pass through a similar slit. — **Figure 3.** The transverse oscillations in one 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 cake horizontally polarized waves.

The Sun and many other low-cal sources produce waves that are randomly polarized (meet Effigy 4). Such light is said to be unpolarized considering 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, allowing just polarization in ane direction to pass through. Polarizing filters are equanimous of long molecules aligned in one direction. Thinking of the molecules as many slits, analogous to those for the oscillating ropes, we can sympathise why but light with a specific polarization can go through. The axis of a polarizing filter is the direction along which the filter passes the electric field of an EM wave (see Figure 5).

The figure shows a slender arrow pointing out of the page and to the right; it is labeled direction of ray (of propagation). At a point on this ray, eight bold arrows point in different directions, perpendicularly away from the ray. These arrows are labeled E.

The figure shows a slender arrow pointing out of the page and to the right that is labeled direction of ray. At the left end of the ray are eight blue arrows emanating from a point on the ray. These arrows are all in a plane perpendicular to the ray and are symmetrically oriented in the perpendicular plane. They are labeled E. Farther to the right on the same ray is a thin rectangle labeled polarizing filter that is in the plane perpendicular to the ray. This filter has seven vertical lines that are equally spaced on its surface. It also has a vertical double headed arrow on its surface that is labeled axis. Still farther along the ray is a single blue double headed arrow oriented vertically that is labeled E and direction of polarization.

Effigy 6 shows the effect of two polarizing filters on originally unpolarized lite. The first filter polarizes the lite along its axis. When the axes of the start and second filters are aligned (parallel), and so all of the polarized light passed by the beginning filter is also passed by the second. If the 2d polarizing filter is rotated, only the component of the lite parallel to the second filter'due south axis is passed. When the axes are perpendicular, no light is passed by the second.

Only the component of the EM wave parallel to the axis of a filter is passed. Let us phone call the angle between the direction of polarization and the axis of a filterθ. If the electric field has an amplitude E, and then the transmitted office of the wave has an aamplitudeEcosθ (see Figure 7). Since the intensity of a wave is proportional to its amplitude squared, the intensity Iof the transmitted wave is related to the incident wave by

I = I₀ cos²θ

where I_ois the intensity of the polarized wave earlier passing through the filter. (The higher up equation is known every bit Malus's law.)

This figure has four subfigures. The first three are schematics and the last is a photograph. The first schematic looks much as in the previous figure, except that there is a second polarizing filter on the axis after the first one. The second polarizing filter has its lines aligned parallel to those of the first polarizing filter (i e, vertical). The vertical double headed arrow labeled E that emerges from the first polarizing filter also passes through the second polarizing filter. The next schematic is similar to the first, except that the second polarizing filter is rotated at forty five degrees with respect to the first polarizing filter. The double headed arrow that emerges from this second filter is also oriented at this same angle. It is also noticeably shorter than the other double headed arrows. The third schematic shows the same situation again, except that the second polarizing filter is now rotated ninety degrees with respect to the first polarizing filter. This time, there is no double headed arrow at all after the second polarizing filter. Finally, the last subfigure shows a photo of three circular optical filters placed over a bright colorful pattern. Two of these filters are place next to each other and the third is placed on top of the other two so that the center of the third is at the point where the edges of the two filters underneath touch. Some light passes through where the upper filter overlaps the left-hand underneath filter. Where the upper filter overlaps the right-hand lower filter, no light passes through.

This schematic is another variation of the schematic first introduced two figures prior. To the left of the vertically oriented polarizing filter is a double headed blue arrow oriented in the plane perpendicular to the propagation direction and at an angle theta with the vertical. After the polarizing filter a smaller vertical double headed arrow appears, which is labeled E cosine theta.

Case 1: Calculating Intensity Reduction by a Polarizing Filter

What bending is needed between the direction of polarized light and the centrality of a polarizing filter to reduce its intensity past 90.0 %?

Strategy

When the intensity is reduced past 90.0% information technology is 10% or 0.100 times its original value. That is, I = 0.100 I₀ . Using this data, the equation I = I₀ cos^twoθ tin exist used to solve for the needed angle.

Solution

Solving the equationI = I₀ cos²θ forcosθ and substituting with the relationship between Iand I₀ gives

$\boldsymbol{ \textbf{cos} \;\theta = \sqrt{\frac{I}{I_0}} {=} \sqrt{\frac{0.100I_0}{I_0}} = 0.3162 }$

Solving for θ yields

θ = cos ^-ane(0.3162) = 71.6^o

Discussion

A fairly large angle between the direction of polarization and the filter centrality is needed to reduce the intensity to10.0% of its original value. This seems reasonable based on experimenting with polarizing films. It is interesting that, at an angle of 45 ^o , the intensity is reduced to50% of its original value (as yous will testify in this section'due south Issues & Exercises). Note that 71.vi ^o is 18.four ^o from reducing the intensity to zip, and that at an angle of xviii.4^o the intensity is reduced to ninety.0% of its original value (as you will too show in Bug & Exercises), giving bear witness of symmetry.

Polarization by Reflection

By now you can probably guess that Polaroid sunglasses cut the glare in reflected lite because that calorie-free is polarized. Y'all can bank check this for yourself by holding Polaroid sunglasses in front of you and rotating them while looking at light reflected from h2o or glass. As yous rotate the sunglasses, you will notice the light gets vivid and dim, but not completely black. This implies the reflected low-cal is partially polarized and cannot be completely blocked by a polarizing filter.

Figure 8 illustrates what happens when unpolarized lite is reflected from a surface. Vertically polarized light is preferentially refracted at the surface, so that the reflected calorie-free is left more horizontally polarized. The reasons for this miracle are beyond the scope of this text, but a convenient mnemonic for remembering this is to imagine the polarization management to exist like an pointer. Vertical polarization would be similar an pointer perpendicular to the surface and would be more likely to stick and non exist reflected. Horizontal polarization is similar an arrow bouncing on its side and would be more than probable to be reflected. Sunglasses with vertical axes would then block more reflected light than unpolarized calorie-free from other sources.

The schematic shows a block of glass in air. A ray labeled unpolarized light starts at the upper left and impinges on the center of the block. Centered on this ray is a symmetric star burst pattern of double headed arrows. From this point where this ray hits the glass block there emerges a reflected ray that goes up and to the right and a refracted ray that goes down and to the right. Both of these rays are labeled partially polarized light. The reflected ray has evenly spaced large black dots on it that are labeled perpendicular to plane of paper. Centered on each black dot is a double headed arrow that is rather short and is perpendicular to the ray. The refracted ray also has evenly spaced dots, but they are much smaller. Centered on each of these small black dots are quite large doubled headed arrows that are perpendicular to the refracted ray.

Since the role 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 exist shown that reflected light is completely polarized at a angle of reflection θ_b , given past

$\boldsymbol{ {tan} \; \theta _b = \frac{n_2}{n_1}},$

where north₁ is the medium in which the incident and reflected calorie-free travel and n₂ is the index of refraction of the medium that forms the interface that reflects the calorie-free. This equation is known as Brewster's law, andθ_b is known as Brewster's angle, named subsequently the 19th-century Scottish physicist who discovered them.

Things Great and Small-scale: Atomic Explanation of Polarizing Filters

Polarizing filters have a polarization axis that acts as a slit. This slit passes electromagnetic waves (oftentimes visible light) that have an electric field parallel to the axis. This is achieved with long molecules aligned perpendicular to the axis as shown in Effigy 9.

The schematic shows a stack of long identical horizontal molecules. A vertical axis is drawn over the molecules.

Effigy ten 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, information technology tin can absorb free 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 motion perpendicular to the molecule. Thus, the electrons tin 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 laissez passer. Thus the centrality of the polarizing filter is perpendicular to the length of the molecule.

The figure contains two schematics. The first schematic shows a long molecule. An EM wave goes through the molecule. The ray of the EM wave is at ninety degrees to the molecular axis and the electric field of the EM wave oscillates along the molecular axis. After passing the long molecule, the magnitude of the oscillations of the EM wave are significantly reduced. The second schematic shows a similar drawing, except that the EM wave oscillates perpendicular to the axis of the long molecule. After passing the long molecule, the magnitude of the oscillation of the EM wave is unchanged.

Case ii: Calculating Polarization past Reflection

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

Strategy

All nosotros demand to solve these problems are the indices of refraction. Air has n₁ = 1.00, h2o has northward_two = 1.333, and crown drinking glass has n'₂ = i.520. The equation $\boldsymbol{\textbf{tan} \;\theta_{b}} = \frac{n_2}{n_1}}$ tin be straight applied to discoverθ_b in each example.

Solution for (a)

Putting the known quantities into the equation

tanθ_b = n₂/n_i

gives

tanθ_b = n₂/north_ane = (1.333)/(1.00) = 1.33

Solving for the angleθ_b yields

θ_b = tan -ane (i.333) = 53.1^o

Solution for (b)

Similarly, for crown glass and air,

$\boldsymbol{ \textbf{tan} \;{\theta ^{\prime}}_{b}} { = } \frac{{n^{\prime}}_2}{n_1}} {=} \frac{1.520}{1.00}} = 1.52 }.$

Thus,

θ'_b = tan^-ane (i.52) = 56.seven^o

Discussion

Light reflected at these angles could be completely blocked by a good polarizing filter held with its axis vertical. Brewster's angle for h2o and air are like to those for glass and air, and then that sunglasses are equally constructive for light reflected from either water or glass nether 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. Information technology will not be completely polarized vertically, because only a small fraction of the incident light is reflected, and then a meaning amount of horizontally polarized low-cal is refracted.

Polarization by Scattering

If yous concord your Polaroid sunglasses in front of you lot and rotate them while looking at blue sky, y'all will see the sky get brilliant and dim. This is a clear indication that light scattered by air is partially polarized. Figure 11 helps illustrate how this happens. Since calorie-free is a transverse EM wave, it vibrates the electrons of air molecules perpendicular to the management information technology is traveling. The electrons then radiate like small antennae. Since they are oscillating perpendicular to the direction of the lite 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, equally in Figure 11, at that place can be no polarization in the scattered light parallel to the original ray, because that would require the original ray to exist 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 but be partially polarized. Furthermore, multiple scattering can bring light to your optics from other directions and can contain dissimilar polarizations.

The schematic shows a ray labeled unpolarized sunlight coming horizontally from the left along what we shall call the x axis. On this ray is a symmetric star burst pattern of double headed arrows, with all the arrows in the plane perpendicular to the ray, This ray strikes a dot labeled molecule. From the molecule three rays emerge. One ray goes straight down, in the negative y direction. It is labeled polarized light and has a single double headed arrow on it that is perpendicular to the plane of the page, that is, the double headed arrow is parallel to the z axis. A second ray continues from the molecule in the same direction as the incoming ray and is labeled unpolarized light. This ray also has a symmetric star burst pattern of double headed arrows on it. A final ray comes out of the plane of the paper in the x z plane, at about 45 degrees from the x axis. This ray is labeled partially polarized light and has a nonsymmetric star burst pattern of double headed arrows on it.

Photographs of the sky can be darkened past polarizing filters, a play tricks used by many photographers to brand clouds brighter by contrast. Scattering from other particles, such every bit smoke or dust, can besides polarize light. Detecting polarization in scattered EM waves can be a useful belittling tool in determining the scattering source.

There is a range of optical furnishings used in sunglasses. Too being Polaroid, other sunglasses accept coloured pigments embedded in them, while others use non-cogitating or fifty-fifty 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, merely become clear in artificial lighting with no UV.

Take-Dwelling Experiment: Polarization

Observe Polaroid sunglasses and rotate 1 while holding the other even so and look at unlike surfaces and objects. Explain your observations. What is the divergence in angle from when y'all see a maximum intensity to when you see a minimum intensity? Observe a reflective glass surface and do the aforementioned. At what angle does the glass demand to exist oriented to give minimum glare?

Liquid Crystals and Other Polarization Furnishings in Materials

While you are undoubtedly aware of liquid crystal displays (LCDs) found in watches, calculators, reckoner screens, cellphones, apartment screen televisions, and other myriad places, you may not be enlightened that they are based on polarization. Liquid crystals are and so named because their molecules tin be aligned even though they are in a liquid. Liquid crystals have the belongings that they can rotate the polarization of light passing through them past 90^o. Furthermore, this property tin be turned off by the awarding of a voltage, as illustrated in Figure 12. It is possible to manipulate this feature quickly and in small-scale well-defined regions to create the contrast patterns we see in and then many LCD devices.

In flat screen LCD televisions, there is a large calorie-free 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 12 (a) and (b). Each unit has three cells, with crimson, 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 tin can vary the picture contrast by varying the forcefulness of the voltage applied to the liquid crystal.

The figure contains two schematics and one photograph. The first schematic shows a ray of initially unpolarized light going through a vertical polarizer, then an element labeled L C D no voltage ninety degree rotation, then finally a horizontal polarizer. The initially unpolarized light becomes vertically polarized after the vertical polarizer, then is rotated ninety degrees by the L C D element so that it is horizontally polarized, then it passes through the horizontal polarizer. The second schematic is the same except that the L C D element is labeled voltage on, no rotation. The light coming out of the L C D element is thus vertically polarized and does not pass through the horizontal polarizer. Finally, a photograph is shown of a laptop computer that is open so that you can see its screen, which is on and has some icons and windows visible.

Many crystals and solutions rotate the plane of polarization of light passing through them. Such substances are said to be optically agile. Examples include carbohydrate water, insulin, and collagen (see Figure 13). In improver to depending on the type of substance, the amount and direction of rotation depends on a number of factors. Amongst these is the concentration of the substance, the distance the calorie-free travels through it, and the wavelength of light. Optical activeness is due to the asymmetric shape of molecules in the substance, such as being helical. Measurements of the rotation of polarized calorie-free passing through substances tin can thus be used to measure out concentrations, a standard technique for sugars. It tin as well give information on the shapes of molecules, such every bit proteins, and factors that affect their shapes, such as temperature and pH.

The schematic shows an initially unpolarized ray of light that passes through three optical elements. The first is a vertical polarizer, so the electric field is vertical after the ray passes through it. Next comes a block that is labeled optically active. Following this block the electric field has been rotated by an angle theta with respect to the vertical. In the schematic this angle is about forty five degrees. Finally, the ray passes through another vertical polarizer that is labeled analyzer. A shorter and vertically oriented electric field appears after this element.

Glass and plastic go optically active when stressed; the greater the stress, the greater the consequence. Optical stress analysis on complicated shapes can be performed past 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 likewise equally stress. The wavelength dependence is sometimes likewise used for artistic purposes.

The figure shows a photograph of a transparent circular plastic lens that is being pinched between clamp fingers. The lens is deformed and rainbows of colors are visible whose outlines roughly follow the deformation of the object.

Some other interesting phenomenon associated with polarized calorie-free is the ability of some crystals to split an unpolarized axle of light into two. Such crystals are said to be birefringent (run into Figure 15). Each of the separated rays has a specific polarization. One behaves commonly and is called the ordinary ray, whereas the other does not obey Snell's police and is called the extraordinary ray. Birefringent crystals tin can be used to produce polarized beams from unpolarized light. Some birefringent materials preferentially absorb i of the polarizations. These materials are called dichroic and can 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 properties of materials related to polarization.

The schematic shows an unpolarized ray of light incident on a block of transparent material The ray is perpendicular to the face of the material. Upon entering the material, part of the ray continues straight on. This ray is horizontally polarized and is labeled o. Another part of the incident ray is deviated at an angle upon entering the material. This ray is vertically polarized and is labeled e.

If you lot prefer to spotter a video, this is a nice one that explains the theory, from the Khan Academy.

Hither is a dainty video where you can these effects.

Section Summary

Polarization is the attribute that wave oscillations have a definite direction 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 it through a polarizing filter or other polarizing material. The intensityI of polarized light after passing through a polarizing filter is I = I_o cos² θ , where I_o is the original intensity and θ is the angle between the direction of polarization and the axis of the filter.
Polarization is also produced past reflection.
Brewster's law states that reflected calorie-free volition exist completely polarized at the angle of reflectionθ_b , known every bit Brewster's bending, given by a statement known as Brewster's constabulary:tanθ_b = n₂/n_one, wheren_ane is the medium in which the incident and reflected calorie-free travel and due north_two is the index of refraction of the medium that forms the interface that reflects the light.
Polarization can also be 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 low-cal inverse by reflection? Is the phase related to polarization?

2: Can a sound wave in air be polarized? Explain.

3: No low-cal passes through two perfect polarizing filters with perpendicular axes. However, if a third polarizing filter is placed between the original 2, some light can laissez passer. Why is this? Nether what circumstances does most of the calorie-free pass?

4: Explain what happens to the free energy carried by calorie-free that it is dimmed past passing it through two crossed polarizing filters.

five: When particles scattering light are much smaller than its wavelength, the amount of scattering is proportional to1/ λ ⁴. Does this hateful there is more than scattering for smallλ than bigλ? How does this relate to the fact that the sky is blue? Hint: red lite has a wavelength of about 650 nm while blueish light has a wavelength of about 400 nm.

vi: Using the data given in the preceding question, explicate why sunsets are red.

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 volition be refracted into the surface. Draw how you lot would do an experiment to determine the polarization of the refracted light. What direction would you lot expect the polarization to have and would y'all await information technology to be 100 %?

Problems & Exercises

1: What angle is needed betwixt the management of polarized light and the axis of a polarizing filter to cut its intensity in half?

two: The bending between the axes of two polarizing filters is 45.0 degrees. Past how much does the second filter reduce the intensity of the light coming through the first?

three: If you have completely polarized calorie-free of intensity 150 W/m² what will its intensity exist afterward passing through a polarizing filter with its axis at an 89.0^o angle to the light'south polarization direction?

4: What bending would the axis of a polarizing filter demand to make with the management of polarized light of intensity 1.00 kW/m² to reduce the intensity to 10.0W/m²?

5: At the stop of Example 1, it was stated that the intensity of polarized calorie-free is reduced to 90.0% of its original value past passing through a polarizing filter with its axis at an angle of 18.4 degrees to the direction of polarization. Verify this argument.

vi: Show that if you accept three polarizing filters, with the 2nd at an bending of 45 ^o to the first and the tertiary at an angle of 90.0 ^o to the beginning, the intensity of light passed by the kickoff volition be reduced to 25.0% of its value. (This is in contrast to having simply the first and 3rd, which reduces the intensity to zero, and so that placing the second between them increases the intensity of the transmitted light.)

8: At what angle will light reflected from diamond exist completely polarized? Think that n diamond = 2.42.

9: What is Brewster's angle for lite traveling in water that is reflected from crown glass? n crown glass = 1.33

ten: A scuba diver sees calorie-free reflected from the h2o's surface. At what angle will this light be completely polarized?

11: At what bending is light inside crown glass completely polarized when reflected from water, every bit in a fish tank?

12: Light reflected at 55.6^o from a window is completely polarized. What is the window's index of refraction and the likely substance of which it is made?

13: (a) Calorie-free reflected at 62.5^o from a gemstone in a ring is completely polarized. Tin the jewel exist a diamond? (b) At what angle would the light exist completely polarized if the gem was in water?

14: If θ_b is Brewster's angle for lite reflected from the acme of an interface betwixt two substances, andθ_b' is Brewster's bending for calorie-free reflected from below, testify thatθ_b+ θ_b _'= 90^o..

15: Integrated Concepts

If a polarizing filter reduces the intensity of polarized light to 50.0 % of its original value, by how much are the electric and magnetic fields reduced?

16: Integrated Concepts

Suppose you put on 2 pairs of Polaroid sunglasses with their axes at an angle of 15.0 ^o . How much longer will information technology take the light to deposit a given amount of energy in your eye compared with a single pair of sunglasses? Assume the lenses are clear except for their polarizing characteristics.

17: Integrated Concepts

(a) On a twenty-four hour period when the intensity of sunlight is one.00 kW/mⁱⁱ, a circular lens 0.200 m in diameter focuses low-cal onto h2o in a black beaker. Two polarizing sheets of plastic are placed in front of the lens with their axes at an angle of 20.0^o. 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 information technology is fourscore.0% absorbed? The aluminum beaker has a mass of 30.0 grams and contains 250 grams of water. (b) Do the polarizing filters get hot? Explain.

Glossary

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

birefringent: crystals that split an unpolarized beam of low-cal into ii beams

Brewster's angle: $\boldsymbol{ \theta _b = \;\textbf{tan}^{-1} \frac{n_2}{n_1}}$ , where north₂ is the index of refraction of the medium from which the light is reflected and n1n1 is the index of refraction of the medium in which the reflected light travels

Brewster's law: tan θ_b = northward₂/north_ane , where due north₁ is the medium in which the incident and reflected light travel and due north₂ is the index of refraction of the medium that forms the interface that reflects the light

management of polarization: the direction parallel to the electrical field for EM waves

horizontally polarized: the oscillations are in a horizontal plane

optically active: substances that rotate the plane of polarization of calorie-free passing through them

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

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

reflected light that is completely polarized: light reflected at the angle of reflectionθ_bknown as Brewster's angle

unpolarized: waves that are randomly polarized

vertically polarized: the oscillations are in a vertical airplane

Solutions

Issues & Exercises

1: 45.0 degrees

3: 45.7 mW/mⁱⁱ

five: 90.0 %

7: I_o

9: 48.8 degrees

xi: 41.ii degrees

thirteen: (a) ane.92, not diamond (Zircon) (b) 55.2 degrees

15: B_ii = 0.707 B₁

17: (a) ii.07 x10^{-2 o}C/southward (b) Yes, the polarizing filters get hot because they absorb some of the lost energy from the sunlight.