Learning Objectives
By the end of this section, you will be able to do the following:
- Discuss the meaning of polarization
- Discuss the property of optical activity of certain materials
The information presented in this section supports the following AP® learning objectives and science practices:
- 6.A.1.3 The student is able to analyze data or a visual representation to identify patterns that indicate that a particular mechanical wave is polarized and construct an explanation of the fact that the wave must have a vibration perpendicular to the direction of energy propagation. (S.P. 5.1, 6.2)
Polarized sunglasses are familiar to most of us. They have a special ability to cut the glare of light reflected from water or glass (see Figure 10.36). Polarized sunglasses 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.
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 (see Figure 10.37). 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 10.37.
To examine this further, consider the transverse waves in the ropes shown in Figure 10.38. 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.
The sun and many other light sources produce waves that are randomly polarized (see Figure 10.39). Such light is said to be unpolarized because it is composed of many waves with all possible directions of polarization. Polarized materials, invented by 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 (see Figure 10.40).
Figure 10.41 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.
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 If the electric field has an amplitude then the transmitted part of the wave has an amplitude (see Figure 10.42). Since the intensity of a wave is proportional to its amplitude squared, the intensity of the transmitted wave is related to the incident wave by
where is the intensity of the polarized wave before passing through the filter. The above equation is known as Malus’s law.
Example 10.8 Calculating Intensity Reduction by a Polarizing Filter
What angle is needed between the direction of polarized light and the axis of a polarizing filter to reduce its intensity by
Strategy
When the intensity is reduced by it is or 0.100 times its original value. That is, Using this information, the equation can be used to solve for the needed angle.
Solution
Solving the equation for and substituting with the relationship between and gives
Solving for yields
Discussion
A fairly large angle between the direction of polarization and the filter axis is needed to reduce the intensity to of its original value. This seems reasonable based on experimenting with polarizing films. It is interesting that, at an angle of the intensity is reduced to of its original value, as you will show in this section’s Problems & Exercises. Note that is from reducing the intensity to zero, and that at an angle of the intensity is reduced to of its original value, as you will also show in Problems & Exercises, giving evidence of symmetry.