How does polarized light act

The angle between the axes of two polarizing filters is. By how much does the second filter reduce the intensity of the light coming through the first?

Two polarizing sheets and are placed together with their transmission axes oriented at an angle to each other.

What is when only of the maximum transmitted light intensity passes through them? Suppose that in the preceding problem the light incident on is unpolarized. At the determined value of , what fraction of the incident light passes through the combination? What angle would the axis of a polarizing filter need to make with the direction of polarized light of intensity to reduce the intensity to?

At the end of Figure , it was stated that the intensity of polarized light is reduced to of its original value by passing through a polarizing filter with its axis at an angle of to the direction of polarization.

Verify this statement. Show that if you have three polarizing filters, with the second at an angle of to the first and the third at an angle of to the first, the intensity of light passed by the first will be reduced to of its value. This is in contrast to having only the first and third, which reduces the intensity to zero, so that placing the second between them increases the intensity of the transmitted light. Three polarizing sheets are placed together such that the transmission axis of the second sheet is oriented at to the axis of the first, whereas the transmission axis of the third sheet is oriented at in the same sense to the axis of the first.

What fraction of the intensity of an incident unpolarized beam is transmitted by the combination? What is the refractive index of the plastic? Use this time to calculate the speed of light. The distance from the wheel to the mirror was Assuming he measured the speed of light accurately, what was the angular velocity of the wheel? Suppose you have an unknown clear substance immersed in water, and you wish to identify it by finding its index of refraction.

You arrange to have a beam of light enter it at an angle of , and you observe the angle of refraction to be. What is the index of refraction of the substance and its likely identity? Shown below is a ray of light going from air through crown glass into water, such as going into a fish tank.

Calculate the amount the ray is displaced by the glass given that the incident angle is and the glass is 1. Considering the previous problem, show that is the same as it would be if the second medium were not present. At what angle is light inside crown glass completely polarized when reflected from water, as in a fish tank? Light reflected at from a window is completely polarized. Can the gem be a diamond? The gem is not a diamond it is zircon. Unreasonable results Suppose light travels from water to another substance, with an angle of incidence of and an angle of refraction of.

We cannot have , since this would imply a speed greater than c. The refracted angle is too big relative to the angle of incidence. Unreasonable results Light traveling from water to a gemstone strikes the surface at an angle of and has an angle of refraction of.

Suppose you put on two pairs of polarizing sunglasses with their axes at an angle of. How much longer will it 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. Two polarizing sheets of plastic are placed in front of the lens with their axes at an angle of.

Assuming the sunlight is unpolarized and the polarizers are efficient, what is the initial rate of heating of the water in , assuming it is. The aluminum beaker has a mass of Light shows staged with lasers use moving mirrors to swing beams and create colorful effects.

Show that a light ray reflected from a mirror changes direction by when the mirror is rotated by an angle. Taking the boundary between nearly empty space and the atmosphere to be sudden, calculate the angle of refraction for sunlight. This lengthens the time the Sun appears to be above the horizon, both at sunrise and sunset.

Now construct a problem in which you determine the angle of refraction for different models of the atmosphere, such as various layers of varying density. Your instructor may wish to guide you on the level of complexity to consider and on how the index of refraction varies with air density. First part:. The remainder depends on the complexity of the solution the reader constructs.

A light ray entering an optical fiber surrounded by air is first refracted and then reflected as shown below. Show that if the fiber is made from crown glass, any incident ray will be totally internally reflected. A light ray falls on the left face of a prism see below at the angle of incidence for which the emerging beam has an angle of refraction at the right face.

Show that the index of refraction n of the glass prism is given by. If and the base angles of the prism are each what is n? If the apex angle in the previous problem is and , what is the value of? The light incident on polarizing sheet is linearly polarized at an angle of with respect to the transmission axis of. Sheet is placed so that its axis is parallel to the polarization axis of the incident light, that is, also at with respect to.

What is the ratio of this maximum intensity to the intensity of transmitted light when is at with respect to? Prove that if I is the intensity of light transmitted by two polarizing filters with axes at an angle and is the intensity when the axes are at an angle then the original intensity. Hint: Use the trigonometric identities and. Skip to content The Nature of Light. 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 figure was taken with a polarizing filter and part a was not. As a result, the reflection of clouds and sky observed in part a is not observed in part b. Polarizing sunglasses are particularly useful on snow and water. An EM wave, such as light, is a transverse wave. The electric and magnetic fields are perpendicular to the direction of propagation.

The direction of polarization of the wave is the direction of the electric field. The radiated light is scattered at right angles to the direction of sunlight propagation, and is polarized either vertically or horizontally, depending upon the direction of scatter. A majority of the polarized light impacting the Earth is polarized horizontally over 50 percent , a fact that can be confirmed by viewing the sky through a Polaroid filter.

Reports have surfaced that certain species of insects and animals are able to detect polarized light, including ants, fruit flies, and certain fish, although the list may actually be much longer.

For example, several insect species primarily honeybees are thought to employ polarized light in navigating to their destinations. It is also widely believed that some individuals are sensitive to polarized light, and are able to observe a yellow horizontal line superimposed on the blue sky when staring in a direction perpendicular to the sun's direction a phenomenon termed Haidinger's brush. Yellow pigment proteins, termed macula lutea , which are dichroic crystals residing in the fovea of the human eye, are credited with enabling a person to view polarized light.

In linearly polarized light, the electric vector is vibrating in a plane that is perpendicular to the direction of propagation, as discussed above. Natural light sources, such as sunlight, and artificial sources, including incandescent and fluorescent light, all emit light with orientations of the electric vector that are random in space and time.

Light of this type is termed non-polarized. In addition, there exist several states of elliptically polarized light that lie between linear and non-polarized, in which the electric field vector transcribes the shape of an ellipse in all planes perpendicular to the direction of light wave propagation. Elliptical polarization, unlike plane-polarized and non-polarized light, has a rotational "sense" that refers to the direction of electric vector rotation around the propagation incident axis of the light beam.

When viewed end-on, the direction of polarization can be either left-handed or right-handed, a property that is termed the handedness of the elliptical polarization. Clockwise rotational sweeps of the vector are referred to as right-handed polarization, and counterclockwise rotational sweeps represent left-handed polarization. In cases where the major and minor vectorial axes of the polarization ellipse are equal, then the light wave falls into the category of circularly polarized light, and can be either right-handed or left-handed in sense.

Another case often occurs in which the minor axis of the electric vector component in elliptically polarized light goes to zero, and the light becomes linearly polarized. Although each of these polarization motifs can be achieved in the laboratory with the appropriate optical instrumentation, they also occur to varying, but minor, degrees in natural non-polarized light.

The ordinary and extraordinary light waves generated when a beam of light traverses a birefringent crystal have plane-polarized electric vectors that are mutually perpendicular to each other. In addition, due to differences in electronic interaction that each component experiences during its journey through the crystal, a phase shift usually occurs between the two waves. Although the ordinary and extraordinary waves follow separate trajectories and are widely separated in the calcite crystal described previously, this is not usually the case for crystalline materials having an optical axis that is perpendicular to the plane of incident illumination.

A special class of materials, known as compensation or retardation plates, are quite useful in producing elliptically and circularly polarized light for a number of applications, including polarized optical microscopy. These birefringent substances are chosen because, when their optical axis is positioned perpendicular to the incident light beam, the ordinary and extraordinary light rays follow identical trajectories and exhibit a phase difference that is dependent upon the degree of birefringence.

Because the pair of orthogonal waves is superimposed, it can be considered a single wave having mutually perpendicular electrical vector components separated by a small difference in phase. When the vectors are combined by simple addition in three-dimensional space, the resulting wave becomes elliptically polarized. This concept is illustrated in Figure 8 , where the resultant electric vector does not vibrate in a single plane, but progressively rotates around the axis of light wave propagation, sweeping out an elliptical trajectory that appears as a spiral when the wave is viewed at an angle.

The size of the phase difference between the ordinary and extraordinary waves of equal amplitude determines whether the vector sweeps an elliptical or circular pathway when the wave is viewed end-on from the direction of propagation. If the phase shift is either one-quarter or three-quarters of a wavelength, then a circular spiral is scribed by the resultant vector. However, phase shifts of one-half or a full wavelength produce linearly polarized light, and all other phase shifts produce sweeps having various degrees of ellipticity.

When the ordinary and extraordinary waves emerge from a birefringent crystal, they are vibrating in mutually perpendicular planes having a total intensity that is the sum of their individual intensities.

Because the polarized waves have electric vectors that vibrate in perpendicular planes, the waves are not capable of undergoing interference. This fact has consequences in the ability of birefringent substances to produce an image. Interference can only occur when the electric vectors of two waves vibrate in the same plane during intersection to produce a change in amplitude of the resultant wave a requirement for image formation.

Therefore, transparent specimens that are birefringent will remain invisible unless they are examined between crossed polarizers, which pass only the components of the elliptically and circularly polarized waves that are parallel to the axis of the polarizer closest to the observer. These components are able to produce amplitude fluctuations to generate contrast and emerge from the polarizer as linearly polarized light.

One of the most common and practical applications of polarization is the liquid crystal display LCD used in numerous devices including wristwatches, computer screens, timers, clocks, and a host of others. These display systems are based upon the interaction of rod-like liquid crystalline molecules with an electric field and polarized light waves. The liquid crystalline phase exists in a ground state that is termed cholesteric , in which the molecules are oriented in layers, and each successive layer is slightly twisted to form a spiral pattern Figure 9.

When polarized light waves interact with the liquid crystalline phase the wave is "twisted" by an angle of approximately 90 degrees with respect to the incident wave. The exact magnitude of this angle is a function of the helical pitch of the cholesteric liquid crystalline phase, which is dependent upon the chemical composition of the molecules it can be fine-tuned by small changes to the molecular structure.

An excellent example of the basic application of liquid crystals to display devices can be found in the seven-segment liquid crystal numerical display illustrated in Figure 9. Here, the liquid crystalline phase is sandwiched between two glass plates that have electrodes attached, similar to those depicted in the illustration. In Figure 9 , the glass plates are configured with seven black electrodes that can be individually charged these electrodes are transparent to light in real devices.

Light passing through polarizer 1 is polarized in the vertical direction and, when no current is applied to the electrodes, the liquid crystalline phase induces a 90 degree "twist" of the light that enables it to pass through polarizer 2, which is polarized horizontally and is oriented perpendicular to polarizer 1. This light can then form one of the seven segments on the display.

When current is applied to the electrodes, the liquid crystalline phase aligns with the current and loses the cholesteric spiral pattern. Light passing through a charged electrode is not twisted and is blocked by polarizer 2. By coordinating the voltage on the seven positive and negative electrodes, the display is capable of rendering the numbers 0 through 9.

In this example the upper right and lower left electrodes are charged and block light passing through them, allowing formation of the number "2" by the display device seen reversed in the figure. 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. Light is one type of electromagnetic EM wave. 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.

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.

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. 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. 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. When the axes are perpendicular, no light is passed by the second filter. Only the component of the EM wave parallel to the axis of a filter is passed. 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.

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. What angle is needed between the direction of polarized light and the axis of a polarizing filter to reduce its intensity by When the intensity is reduced by A fairly large angle between the direction of polarization and the filter axis is needed to reduce the intensity to This seems reasonable based on experimenting with polarizing films.

Note that For our purposes, it is sufficient to merely say that an electromagnetic wave is a transverse wave that has both an electric and a magnetic component. The transverse nature of an electromagnetic wave is quite different from any other type of wave that has been discussed in The Physics Classroom Tutorial.

Let's suppose that we use the customary slinky to model the behavior of an electromagnetic wave. As an electromagnetic wave traveled towards you, then you would observe the vibrations of the slinky occurring in more than one plane of vibration. This is quite different than what you might notice if you were to look along a slinky and observe a slinky wave traveling towards you. Indeed, the coils of the slinky would be vibrating back and forth as the slinky approached; yet these vibrations would occur in a single plane of space.

That is, the coils of the slinky might vibrate up and down or left and right. Yet regardless of their direction of vibration, they would be moving along the same linear direction as you sighted along the slinky. If a slinky wave were an electromagnetic wave, then the vibrations of the slinky would occur in multiple planes. Unlike a usual slinky wave, the electric and magnetic vibrations of an electromagnetic wave occur in numerous planes. A light wave that is vibrating in more than one plane is referred to as unpolarized light.

Light emitted by the sun, by a lamp in the classroom, or by a candle flame is unpolarized light. Such light waves are created by electric charges that vibrate in a variety of directions, thus creating an electromagnetic wave that vibrates in a variety of directions. This concept of unpolarized light is rather difficult to visualize. In general, it is helpful to picture unpolarized light as a wave that has an average of half its vibrations in a horizontal plane and half of its vibrations in a vertical plane.

It is possible to transform unpolarized light into polarized light. Polarized light waves are light waves in which the vibrations occur in a single plane. The process of transforming unpolarized light into polarized light is known as polarization. There are a variety of methods of polarizing light. The four methods discussed on this page are:. The most common method of polarization involves the use of a Polaroid filter.

Polaroid filters are made of a special material that is capable of blocking one of the two planes of vibration of an electromagnetic wave.

Remember, the notion of two planes or directions of vibration is merely a simplification that helps us to visualize the wavelike nature of the electromagnetic wave. In this sense, a Polaroid serves as a device that filters out one-half of the vibrations upon transmission of the light through the filter.

When unpolarized light is transmitted through a Polaroid filter, it emerges with one-half the intensity and with vibrations in a single plane; it emerges as polarized light. A Polaroid filter is able to polarize light because of the chemical composition of the filter material.

The filter can be thought of as having long-chain molecules that are aligned within the filter in the same direction. During the fabrication of the filter, the long-chain molecules are stretched across the filter so that each molecule is as much as possible aligned in say the vertical direction. As unpolarized light strikes the filter, the portion of the waves vibrating in the vertical direction are absorbed by the filter.

The general rule is that the electromagnetic vibrations that are in a direction parallel to the alignment of the molecules are absorbed. The alignment of these molecules gives the filter a polarization axis. This polarization axis extends across the length of the filter and only allows vibrations of the electromagnetic wave that are parallel to the axis to pass through. Any vibrations that are perpendicular to the polarization axis are blocked by the filter.

Thus, a Polaroid filter with its long-chain molecules aligned horizontally will have a polarization axis aligned vertically. Such a filter will block all horizontal vibrations and allow the vertical vibrations to be transmitted see diagram above.