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Physics 212 Lecture 25 Physics 212 Lecture 25, Slide 1 Main Point 1 First, we introduced the law of reflection, that the angle of incidence equals the angle of reflection. We offered a derivation of this relation for plane waves by requiring the phase of the reflected wave across a wavefront perpendicular to the ray to be constant. Physics 212 Lecture 25, Slide 2 Main Point 2 Second, we introduced the modifications to Maxwell’s equations that are necessary to describe electromagnetic fields in matter. By simply replacing e0 and m0 with e and m, we determined that the speed of an electromagnetic wave in matter is less than the speed of light in vacuum. We defined the index of refraction n of a material as the ration of the speed of light in that material to the speed of light in vacuum. For non-magnetic materials, the index of refraction is simply related to the dielectric constant. Physics 212 Lecture 25, Slide 3 Main Point 3 Third, we obtained Snell’s law that relates the angle of refraction to the angle of incidence by requiring the phase of the refracted wave across a wavefront perpendicular to the ray to be constant. Physics 212 Lecture 25, Slide 4 Main Point 4 Finally, we discussed intensities and polarizations of these rays for some special cases. In particular, we determined that for light moving from a medium with higher index of refraction to one with a lower index of refraction, there is a critical angle of incidence, qc equal to the arcsine of the ratio of the indices of refraction, such that for all angles greater than this angle, no light will be refracted; all light will be reflected. We also discussed the partial polarization perpendicular to the plane of incidence of the reflected ray and introduced Brewster’s angle , defined as the arctangent of the ratio of the indices of refraction, for which the polarization is total. Physics 212 Lecture 25, Slide 5 Let’s start with a summary: Physics 212 Lecture 25, Slide 6 The speed of light in a medium is slower than in empty space: vmedium = c / nmedium Since l = v/f, if v decreases then so does l Physics 212 Lecture 25, Slide 7 Physics 212 Lecture 25, Slide 8 A x1 l1 y1 Same Principle works for Light !! D y2 l2 x2 B 2 2 2 2 x1 y1 x2 y 2 Time from A to B : l l t 1 2 v1 v2 v1 v2 To find minimum time, dt x1 x2 dx2 differentiate t wrt x1 and set = 0 dx1 v1 x1 y1 v2 x2 y2 dx1 2 2 2 2 dx2 How is x2 related to x1? x2 D x1 1 dx1 Setting x1 x sin 1 sin 2 2 0 v = c/n n1 sin 1 n2 sin 2 dt/dx1 = 0 v1l1 v2l2 v1 v2 Physics 212 Lecture 25, Slide 9 Physics 212 Lecture 25, Slide 10 A ray of light passes from air into water with an angle of incidence of 30 degrees. Checkpoint 1a Which of the following quantities does not change as the light enters the water? A. wavelength B. frequency C. speed of propagation Physics 212 Lecture 25, Slide 11 A ray of light passes from air into water with an angle of incidence of 30 degrees. Checkpoint 1b Some of the light also reflects off the surface of the water. If the incident light is initially unpolarized, the reflected light will be A. unpolarized B. somewhat horizontally polarized C. somewhat vertically polarized Physics 212 Lecture 25, Slide 12 Physics 212 Lecture 25, Slide 13 The path of light is bent as it passes from medium 1 to medium 2. Checkpoint 2a Compare the indices of refraction in the two media. A. n1 > n2 B. n1 = n2 C. n1 < n2 Physics 212 Lecture 25, Slide 14 A light ray travels in a medium with n1 and completely reflects from the surface of a medium n2. Checkpoint 2b The critical angle depends on: A. n1 only B. n2 only C. both n1 and n2 Physics 212 Lecture 25, Slide 15 Physics 212 Lecture 25, Slide 16 A light is shining at the bottom of a swimming pool (shown in yellow in the figure). A person is standing at the edge of the pool. Checkpoint 3 Can the person standing on the edge of the pool be prevented from seeing the light by total internal reflection at the water-air surface? A. yes B. no Physics 212 Lecture 25, Slide 17 Physics 212 Lecture 25, Slide 18 Reflection Physics 212 Lecture 25, Slide 19 Refraction: Snell’s Law Physics 212 Lecture 25, Slide 20 Physics 212 Lecture 25, Slide 21 Total Internal Reflection 1 > c Total Internal Reflection Physics 212 Lecture 25, Slide 22 Intensity Anything looks like a mirror If two materials have the same n if light is just glancing off it. then its hard to tell them apart. Physics 212 Lecture 25, Slide 23 Exercise 45o A meter stick lies at the bottom of a nwater = 1.33 rectangular water tank of height 50cm. You look into the tank at an angle of 45o relative to vertical along a line that 50 cm skims the top edge of the tank. What is the smallest number on the 0 20 40 60 80 100 ruler that you can see? Conceptual Analysis: Strategy: Physics 212 Lecture 25, Slide 24 Physics 212 Lecture 25, Slide 25 Physics 212 Lecture 25, Slide 26