Physics Lecture 3: Polarization (PDF)

## 3. Polarization ### 3.1 Polarization by Absorption - The most common technique for producing polarized light. - Uses a material (such as tourmaline) that absorbs light vibrations parallel to the axis of the crystal, and transmits vibrations perpendicular to the axis (parallel to transition axi...

## 3. Polarization ### 3.1 Polarization by Absorption - The most common technique for producing polarized light. - Uses a material (such as tourmaline) that absorbs light vibrations parallel to the axis of the crystal, and transmits vibrations perpendicular to the axis (parallel to transition axis). - In 1938, E. H. Land (1909-1991) discovered a material called Polaroid, which polarizes light through selective absorption. - This material is fabricated in thin sheets of long-chain hydrocarbons. > **Figure** ... represents an unpolarized light beam incident on a first polarizing sheet called the polarizer. Because the transmission axis is oriented vertically in the figure, the light transmitted through this sheet is polarized vertically. A second polarizing sheet called the analyzer intercepts the beam. - It is common to refer to the direction perpendicular to the molecular chains (crystal axis) as the transmission axis. - In an ideal polarizer, all light parallel to the transmission axis is transmitted, and all light perpendicular to the transmission axis is absorbed. - **Absorb** - perpendicular to transmission axis (parallel to the axis of the crystal). - **Transmit** - parallel to transmission axis (perpendicular to the axis of the crystal). #### Malus's law - Let the angle between the transmission axis of the polarizer and that of the analyzer be $\theta$. Then, the amount of light $I$ transmitted through the analyzer depends on the value of $\theta$ as follows: $I = I_{max} cos^2(\theta)$ *(Malus's law)* - Where $I_{max}$ is the maximum amount of light transmitted (i.e. the amount transmitted at $\theta = 0$). - If a beam of light is sent through a thin plate of tourmaline, the transmitted beam will be linearly polarized in the direction parallel to the transmission axis. - If this linearly polarized beam is then passed through a second tourmaline plate whose axis is at right angles to the axis of the first (90°), no light will pass through the second crystal. - If the second crystal is rotated so that its axis is parallel to the axis of the first crystal, the polarized beam will pass through the second crystal. - At intermediate positions, the intensity of the transmitted beam will be smaller than that transmitted when the axes are parallel. - The first crystal is called the polarizer. It serves the function of polarizing the light. The second crystal is called the analyzer. ### 3.2 Polarization by Reflection - When an unpolarized light beam is reflected from a surface, the reflected light may be completely polarized, partially polarized, or unpolarized, depending on the angle of incidence: 1. If the angle of incidence is 0°, the reflected beam is unpolarized. 2. Electric field vector can be resolved into two components: - One parallel to the surface (and perpendicular to the page, represented by the dots). - The other (represented by the brown arrows) perpendicular both to the first component and to the direction of propagation. - A partially polarized reflected beam. The refracted beam is also partially polarized. #### Brewster's Law - Suppose the angle of incidence $\theta_i$ is varied until the angle between the reflected and refracted beams is 90°. At this particular angle of incidence, the reflected beam is completely polarized. - The angle of incidence at which this polarization occurs is called the polarizing angle $\theta_p$ (Brewster's Law). - $\theta_p + 90° + \theta _2 = 180°$; $\theta_2 = 90° - \theta_p$ - Using Snell's law of refraction gives: $\frac {sin \theta1}{sin \theta2} = \frac {n2}{n1}$ - Because $sin \theta_2 = sin(90° - \theta_p) = cos \theta_p$ $\frac {n2}{n1} = \frac {sin \theta_p}{cos \theta_p}$ $tan \theta_p = \frac {n2}{n1}$ - The angle of incidence of a light beam onto a reflecting surface is continuously variable. The reflected ray in air is completely polarized when the angle of incidence is 48.0°. What is the index of refraction of the reflecting material? **Solution** - By Brewster's law, for light in air (n = 1.00) reflecting off a surface of index n, $tan \theta_p = \frac {n2}{n1} = \frac {n}{1.00} = n$ $n = tan \theta_p= tan(48.0°) = 1.11$ ### 3.3 Polarization by Scattering - Light can be polarized by scattering from small particles or molecules. - The blue light of the sky caused by scattering from particles or molecules whose diameter is on the order of magnitude of the wavelength of visible light is partially polarized. - One can explain polarization by scattering by sending unpolarized light down a tube of water containing fine particles in suspension. - When light of various wavelengths $\lambda$ is incident on gas molecules of diameter $d$, where $d <<\lambda$, the relative intensity of the scattered light varies as 1/$\lambda^4$. - The condition $d << \lambda$ is satisfied for scattering from oxygen (O2) and nitrogen (N2) molecules in the atmosphere whose diameters are about 0.2 nm - When you look up into the sky in a direction that is not toward the sun, you see the scattered light, which is violet. Your eyes, however, are not very sensitive to violet light. Light of the next color in the spectrum, blue, is scattered with less intensity than violet. ### 3.4 Polarization by Double Refraction - When light travels through an amorphous material such as glass, it travels with a speed that is the same in all directions. - Some transparent crystals, such as calcite and quartz, have the property that when one views an object through them, one sees two images of the object. Such materials are characterized by two indices of refraction. - If one passes a narrow beam of light through them, the refracted beam is split into two parts which travel through the crystal and emerge as two separate beams. - One of the beams obeys the ordinary laws of refraction and is called the ordinary ray. The other beam is called the extraordinary ray. The extraordinary follows different laws. **Note:** The document included handwritten text written in Arabic at the top of page 7 and page 12. I did not include the text in the markdown. The text translates to: - Page 7: Discuss in the oral and drawings. - Page 12: In the exam.