© 2012 Pearson Education, Inc. { Chapter 33 The Nature and Propagation of Light (cont.)

© 2012 Pearson Education, Inc. Dispersion Dispersion: The index of refraction depends on the wavelength of the light. See Figure (right). Dispersion: The index of refraction depends on the wavelength of the light. See Figure (right). Figure (below) shows dispersion by a prism. Figure (below) shows dispersion by a prism.

© 2012 Pearson Education, Inc. Rainbows—I The formation of a rainbow is due to the combined effects of dispersion, refraction, and reflection. (See Figure below and on the next slide.) The formation of a rainbow is due to the combined effects of dispersion, refraction, and reflection. (See Figure below and on the next slide.)

© 2012 Pearson Education, Inc. Rainbows—II

Q33.4 Light passes from a medium of index of refraction n a into a second medium of index of refraction n b. The critical angle for total internal reflection is  crit. In order for total internal reflection to occur, what must be true about n a, n b, and the incident angle  a ? A. n a > n b and  a >  crit B. n a > n b and  a <  crit C. n a  crit D. n a < n b and  a <  crit

© 2012 Pearson Education, Inc. Light passes from a medium of index of refraction n a into a second medium of index of refraction n b. The critical angle for total internal reflection is  crit. In order for total internal reflection to occur, what must be true about n a, n b, and the incident angle  a ? A33.4 A. n a > n b and  a >  crit B. n a > n b and  a <  crit C. n a  crit D. n a < n b and  a <  crit

© 2012 Pearson Education, Inc. Polarization An electromagnetic wave is linearly polarized if the electric field always points along one direction. An electromagnetic wave is linearly polarized if the electric field always points along one direction. Figure at the right shows a Polaroid polarizing filter. Figure at the right shows a Polaroid polarizing filter.

© 2012 Pearson Education, Inc. Malus’s law Figure below shows a polarizer and an analyzer. Figure below shows a polarizer and an analyzer. Malus’s law: I = I max cos 2 . Malus’s law: I = I max cos 2 . Read Problem-Solving Strategy Read Problem-Solving Strategy Follow Example Follow Example 33.5.

© 2012 Pearson Education, Inc. Three polarizing filters are stacked with the polarizing axes of the second and third filters oriented at 45° and 90°, respectively, relative to the polarizing axis of the first filter. Unpolarized light of intensity I 0 is incident on the first filter. The intensity of light emerging from the third filter is Q33.5

© 2012 Pearson Education, Inc. A33.5 Three polarizing filters are stacked with the polarizing axes of the second and third filters oriented at 45° and 90°, respectively, relative to the polarizing axis of the first filter. Unpolarized light of intensity I 0 is incident on the first filter. The intensity of light emerging from the third filter is

© 2012 Pearson Education, Inc. Polarization by reflection When light is reflected at the polarizing angle  p, the reflected light is linearly polarized. See Figure below. When light is reflected at the polarizing angle  p, the reflected light is linearly polarized. See Figure below.

© 2012 Pearson Education, Inc. Brewster’s law Brewster’s law: tan  p = n b /n a. Brewster’s law: tan  p = n b /n a. At the polarizing angle, the reflected and refracted rays are perpendicular to each other. See Figure at the right. At the polarizing angle, the reflected and refracted rays are perpendicular to each other. See Figure at the right.

© 2012 Pearson Education, Inc. Natural light is incident on the surface of a liquid. The reflected light will be completely polarized if the incident angle  a is Q33.6 A. greater than the polarizing angle. B. greater than or equal to the polarizing angle. C. equal to the polarizing angle. D. less than or equal to the polarizing angle. E. less than the polarizing angle.

© 2012 Pearson Education, Inc. Natural light is incident on the surface of a liquid. The reflected light will be completely polarized if the incident angle  a is A33.6 A. greater than the polarizing angle. B. greater than or equal to the polarizing angle. C. equal to the polarizing angle. D. less than or equal to the polarizing angle. E. less than the polarizing angle.

© 2012 Pearson Education, Inc. Circular polarization Circular polarization results from the superposition of two perpendicularly polarized electromagnetic waves having equal amplitude but a quarter-cycle phase difference. The result is that the electric field vector has constant amplitude but rotates about the direction of propagation. (Figure below.) Circular polarization results from the superposition of two perpendicularly polarized electromagnetic waves having equal amplitude but a quarter-cycle phase difference. The result is that the electric field vector has constant amplitude but rotates about the direction of propagation. (Figure below.)

© 2012 Pearson Education, Inc. Scattering of light Scattering occurs when light has been absorbed by molecules and reradiated. Scattering occurs when light has been absorbed by molecules and reradiated. Figure below shows the effect of scattering for two observers. Figure below shows the effect of scattering for two observers.

© 2012 Pearson Education, Inc. Why are clouds white? Clouds are white because they scatter all wavelengths efficiently. See Figure below. Clouds are white because they scatter all wavelengths efficiently. See Figure below.