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27.8 Polarization  (Page 4/19)

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Calculating polarization by reflection

(a) At what angle will light traveling in air be completely polarized horizontally when reflected from water? (b) From glass?

Strategy

All we need to solve these problems are the indices of refraction. Air has n 1 = 1.00, water has n 2 = 1 . 333, size 12{n rSub { size 8{2} } =1 "." "333"} {} and crown glass has n ′ 2 = 1.520 size 12{ { {n}} sup { ' } rSub { size 8{2} } =1 "." "333"} {} . The equation tan θ b = n 2 n 1 size 12{"tan"θ rSub { size 8{b} } = { {n rSub { size 8{2} } } over {n rSub { size 8{1} } } } } {} can be directly applied to find θ b size 12{θ rSub { size 8{b} } } {} in each case.

Solution for (a)

Putting the known quantities into the equation

tan θ b = n 2 n 1 size 12{"tan"θ rSub { size 8{b} } = { {n rSub { size 8{2} } } over {n rSub { size 8{1} } } } } {}

gives

tan θ b = n 2 n 1 = 1.333 1.00 = 1 . 333. size 12{"tan"θ rSub { size 8{b} } = { {n rSub { size 8{2} } } over {n rSub { size 8{1} } } } =1 "." "333"} {}

Solving for the angle θ b size 12{θ rSub { size 8{b} } } {} yields

θ b = tan − 1 1 . 333 = 53 . 1º . size 12{θ rSub { size 8{b} } ="tan" rSup { size 8{ - 1} } 1 "." "333"="53" "." 1°} {}

Solution for (b)

Similarly, for crown glass and air,

tan θ ′ b = n ′ 2 n 1 = 1.520 1.00 = 1 . 52. size 12{"tan {" ital {θ}} sup { ' } rSub { size 8{b} } = { { { {n}} sup { ' } rSub { size 8{2} } } over {n rSub { size 8{1} } } } =1 "." "52"} {}

Thus,

θ ′ b = tan − 1 1 . 52 = 56.7º. size 12{ { {θ}} sup { ' } rSub { size 8{b} } ="tan" rSup { size 8{ - 1} } 1 "." "52"="56" "." 7°} {}

Discussion

Light reflected at these angles could be completely blocked by a good polarizing filter held with its axis vertical . 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 not reflected is refracted into these media. So at an incident angle equal to Brewster’s angle, the refracted light will be slightly polarized vertically. 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.

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Polarization by scattering

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. This is a clear indication that light scattered by air is partially polarized. [link] helps illustrate how this happens. Since light is a transverse EM wave, it vibrates the electrons of air molecules perpendicular to the direction it is traveling. The electrons then radiate like small antennae. 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. When viewing the light along a line perpendicular to the original ray, as in [link] , 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. 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. Furthermore, multiple scattering can bring light to your eyes from other directions and can contain different polarizations.

The schematic shows a ray labeled unpolarized sunlight coming horizontally from the left along what we shall call the x axis. On this ray is a symmetric star burst pattern of double headed arrows, with all the arrows in the plane perpendicular to the ray, This ray strikes a dot labeled molecule. From the molecule three rays emerge. One ray goes straight down, in the negative y direction. It is labeled polarized light and has a single double headed arrow on it that is perpendicular to the plane of the page, that is, the double headed arrow is parallel to the z axis. A second ray continues from the molecule in the same direction as the incoming ray and is labeled unpolarized light. This ray also has a symmetric star burst pattern of double headed arrows on it. A final ray comes out of the plane of the paper in the x z plane, at about 45 degrees from the x axis. This ray is labeled partially polarized light and has a nonsymmetric star burst pattern of double headed arrows on it.
Polarization by scattering. Unpolarized light scattering from air molecules shakes their electrons perpendicular to the direction of the original ray. The scattered light therefore has a polarization perpendicular to the original direction and none parallel to the original direction.

Photographs of the sky can be darkened by polarizing filters, a trick used by many photographers to make clouds brighter by contrast. Scattering from other particles, such as smoke or dust, can also polarize light. Detecting polarization in scattered EM waves can be a useful analytical tool in determining the scattering source.

Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
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Muhammed
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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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