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By the end of this section, you will be able to:
  • Explain the change in intensity as polarized light passes through a polarizing filter
  • Calculate the effect of polarization by reflection and Brewster’s angle
  • Describe the effect of polarization by scattering
  • Explain the use of polarizing materials in devices such as LCDs

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

The figure has two photographs of the same part of a river. In figure a, the clouds and sky are reflected in the water, making it hard to see the stones at the bottom of the river. In figure b, the reflection of the sky is absent and the bottom of the river can be seen more clearly.
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. (credit a and credit b: modifications of work by “Amithshs”/Wikimedia Commons)

Malus’s law

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

A part of an electromagnetic wave moving with velocity c is shown at one instant in time. The two vector components, E and B, are shown and are perpendicular to one another and to the direction of propagation. The vectors representing the magnitude and direction of E, shown as arrows whose tails lie on the line of propagation of the wave, form a sine wave in one plane. Similarly, the B vectors form a sine wave in a plane perpendicular to the E wave. The E and B waves are in phase. The direction of polarization is given by the direction of the E vectors.
An EM wave, such as light, is a transverse wave. The electric ( E ) and magnetic ( B ) fields are perpendicular to the direction of propagation. The direction of polarization of the wave is the direction of the electric field.

To examine this further, consider the transverse waves in the ropes shown in [link] . 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.

Figure a shows waves on a vertically oscillating rope that pass through a vertical slit. The vertical oscillation is the direction of polarization. Figure b shows waves on a horizontally oscillating rope that do not pass through a similar vertical slit. The horizontal oscillation is the direction of polarization.
The transverse oscillations in one rope (a) are in a vertical plane, and those in the other rope (b) 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.

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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