equation for light intensity through polarized filters

The reasons for this phenomenon are beyond the scope of this text, but a convenient mnemonic for remembering this is to imagine the polarization direction to be like an arrow. Vertically polarized light is preferentially refracted at the surface, so that the reflected light is left more horizontally polarized. This implies the reflected light is partially polarized and cannot be completely blocked by a polarizing filter.įigure 27.43 illustrates what happens when unpolarized light is reflected from a surface. As you rotate the sunglasses, you will notice the light gets bright and dim, but not completely black. You can check this for yourself by holding Polaroid sunglasses in front of you and rotating them while looking at light reflected from water or glass. Polarization by Reflectionīy now you can probably guess that Polaroid sunglasses cut the glare in reflected light because that light is polarized. 0% of its original value (as you will also show in Problems & Exercises), giving evidence of symmetry. 4º from reducing the intensity to zero, and that at an angle of 18. It is interesting that, at an angle of 45º 45º, the intensity is reduced to 50% 50% of its original value (as you will show in this section’s Problems & Exercises). This seems reasonable based on experimenting with polarizing films. Since the intensity of a wave is proportional to its amplitude squared, the intensity I I of the transmitted wave is related to the incident wave byĪ fairly large angle between the direction of polarization and the filter axis is needed to reduce the intensity to 10. If the electric field has an amplitude E E, then the transmitted part of the wave has an amplitude E cos θ E cos θ (see Figure 27.42). 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. When the axes are perpendicular, no light is 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 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. The first filter polarizes the light along its axis. The direction of polarization of an EM wave is defined to be the direction of its electric field.įigure 27.41 shows the effect of two polarizing filters on originally unpolarized light. The axis of a polarizing filter is the direction along which the filter passes the electric field of an EM wave (see Figure 27.40).įigure 27.40 A polarizing filter has a polarization axis that acts as a slit passing through electric fields parallel to its 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. Polarizing filters are composed of long molecules aligned in one direction. Polaroid materials, invented by the founder of 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 are randomly polarized (see Figure 27.39). 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 27.37.įigure 27.38 The transverse oscillations in one rope are in a vertical plane, and those in the other rope 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 have a definite direction relative to the direction of propagation of the wave. There are specific directions for the oscillations of the electric and magnetic fields. 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 27.37). Light is one type of electromagnetic (EM) wave. 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 27.36 These two photographs of a river show the effect of a polarizing filter in reducing glare in light reflected from the surface of water.

Equation for light intensity through polarized filters