The axis of the second polarizer is rotated at an angle 0 = 45° from the vertical. The axis of the first polarizer is vertical. Besides being Polaroid, other sunglasses have colored pigments embedded in them, while others use non-reflective or even reflective coatings.(10%) Problem 10: Unpolarized light of intensity lo = 1350 W/m2 is incident upon three polarizers. There is a range of optical effects used in sunglasses. Detecting polarization in scattered EM waves can be a useful analytical tool in determining the scattering source. Scattering from other particles, such as smoke or dust, can also polarize light. Photographs of the sky can be darkened by polarizing filters, a trick used by many photographers to make clouds brighter by contrast. Furthermore, multiple scattering can bring light to your eyes from other directions and can contain different polarizations. Along other directions, a component of the other polarization can be projected along the line of sight, and the scattered light will only be partially polarized. When viewing the light along a line perpendicular to the original ray, as in Figure 11, there can be no polarization in the scattered light parallel to the original ray, because that would require the original ray to be a longitudinal wave. Since they are oscillating perpendicular to the direction of the light ray, they produce EM radiation that is polarized perpendicular to the direction of the ray. The electrons then radiate like small antennae. Since light is a transverse EM wave, it vibrates the electrons of air molecules perpendicular to the direction it is traveling. Figure 11 helps illustrate how this happens. This is a clear indication that light scattered by air is partially polarized. If you hold your Polaroid sunglasses in front of you and rotate them while looking at blue sky, you will see the sky get bright and dim. The scattered light therefore has a polarization perpendicular to the original direction and none parallel to the original direction. Unpolarized light scattering from air molecules shakes their electrons perpendicular to the direction of the original ray. It will not be completely polarized vertically, because only a small fraction of the incident light is reflected, and so a significant amount of horizontally polarized light is refracted. So at an incident angle equal to Brewster’s angle, the refracted light will be slightly polarized vertically. Light not reflected is refracted into these media. Brewster’s angle for water and air are similar to those for glass and air, so that sunglasses are equally effective for light reflected from either water or glass under similar circumstances. Light reflected at these angles could be completely blocked by a good polarizing filter held with its axis vertical. Solving the equation I = I 0 cos 2 θ for cos θ and substituting with the relationship between I and I 0 gives Using this information, the equation I = I 0 cos 2 θ can be used to solve for the needed angle. When the intensity is reduced by 90.0%, it is 10.0% or 0.100 times its original value. What angle is needed between the direction of polarized light and the axis of a polarizing filter to reduce its intensity by 90.0%? Strategy Calculating Intensity Reduction by a Polarizing Filter For EM waves, the direction of the electric field is analogous to the disturbances on the ropes.Įxample 1. However, a vertical slit blocks the horizontally polarized waves. If a vertical slit is placed on the first rope, the waves pass through. Those in the other rope are in a horizontal plane and are horizontally polarized. The oscillations in one rope are in a vertical plane and are said to be vertically polarized. To examine this further, consider the transverse waves in the ropes shown in Figure 3. Thus we can think of the electric field arrows as showing the direction of polarization, as in Figure 2. 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 2). Light is one type of electromagnetic (EM) wave. The electric and magnetic fields are perpendicular to the direction of propagation. An EM wave, such as light, is a transverse wave.

Unpolarized light intensity equation