If the electric field has an amplitude E, then the transmitted part of the wave has an amplitude E cos θ E cos θ ( Figure 1.37). Let us call the angle between the direction of polarization and the axis of a filter θ θ. Only the component of the EM wave parallel to the axis of a filter is passed. Its axis is perpendicular to the filter on the right (dark area) and parallel to the filter on the left (lighter area). (d) In this photograph, a polarizing filter is placed above two others. (c) When the second filter is perpendicular to the first, no light is passed. (b) As the second filter is rotated, only part of the light is passed. (a) All of the polarized light is passed by the second polarizing filter, because its axis is parallel to the first. The axis of a polarizing filter is the direction along which the filter passes the electric field of an EM wave.įigure 1.36 The effect of rotating two polarizing filters, where the first polarizes the light. 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. Polarizing filters are composed of long molecules aligned in one direction. 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. Such light is said to be unpolarized, because it is composed of many waves with all possible directions of polarization. The Sun and many other light sources produce waves that have the electric fields in random directions ( Figure 1.35(a)).

Vertical slits pass vertically polarized waves and block horizontally polarized waves. The first is said to be vertically polarized, and the other is said to be horizontally polarized. Thus, we can think of the electric field arrows as showing the direction of polarization, as in Figure 1.33.įigure 1.34 The transverse oscillations in one rope (a) are in a vertical plane, and those in the other rope (b) are in a horizontal plane.

For an EM wave, we define the direction of polarization to be the direction parallel to the electric field. (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. Polarization is the attribute that a wave’s oscillations do have a definite direction relative to the direction of propagation of the 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. 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 ( Figure 1.33). Light is one type of electromagnetic (EM) wave. (credit a and credit b: modifications of work by “Amithshs”/Wikimedia Commons) Malus’s Law Polarizing sunglasses are particularly useful on snow and water. As a result, the reflection of clouds and sky observed in part (a) is not observed in part (b). Part (b) of this figure was taken with a polarizing filter and part (a) was not. Figure 1.32 These two photographs of a river show the effect of a polarizing filter in reducing glare in light reflected from the surface of water.

Intensity light reflection equation