Physics 212 Lecture 25, Slide 1 Physics 212 Lecture 25

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 e 0 and m 0 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, q c 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

Physics 212 Lecture 25, Slide 6 Let’s start with a summary:

Physics 212 Lecture 25, Slide 7 The speed of light in a medium is slower than in empty space: v medium = c / n medium Since  = v/f, if v decreases then so does 

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Physics 212 Lecture 25, Slide 9 A B x1x1 y1y1 l1l1 x2x2 y2y2 l2l2 Time from A to B : Setting dt/dx 1 = 0 Same Principle works for Light !! To find minimum time, differentiate t wrt x 1 and set = 0 D How is x 2 related to x 1 ? v = c/n

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Physics 212 Lecture 25, Slide 11 Checkpoint 1a A ray of light passes from air into water with an angle of incidence of 30 degrees. Which of the following quantities does not change as the light enters the water? A. wavelengthB. frequencyC. speed of propagation

Physics 212 Lecture 25, Slide 12 Checkpoint 1b A ray of light passes from air into water with an angle of incidence of 30 degrees. 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. unpolarizedB. somewhat horizontally polarizedC. somewhat vertically polarized

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Physics 212 Lecture 25, Slide 14 Checkpoint 2a The path of light is bent as it passes from medium 1 to medium 2. Compare the indices of refraction in the two media. A. n 1 > n 2 B. n 1 = n 2 C. n 1 < n 2

Physics 212 Lecture 25, Slide 15 The critical angle depends on: A. n 1 only B. n 2 onlyC. both n 1 and n 2 A light ray travels in a medium with n 1 and completely reflects from the surface of a medium n 2. Checkpoint 2b

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Physics 212 Lecture 25, Slide 17 Checkpoint 3 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. 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. yesB. no

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Physics 212 Lecture 25, Slide 19 Reflection

Physics 212 Lecture 25, Slide 20 Refraction: Snell’s Law

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Physics 212 Lecture 25, Slide 22 Total Internal Reflection  1 >  c Total Internal Reflection

Physics 212 Lecture 25, Slide 23 Intensity If two materials have the same n then its hard to tell them apart. Anything looks like a mirror if light is just glancing off it.

Physics 212 Lecture 25, Slide cm o A meter stick lies at the bottom of a rectangular water tank of height 50cm. You look into the tank at an angle of 45 o relative to vertical along a line that skims the top edge of the tank. What is the smallest number on the ruler that you can see? n water = 1.33 Conceptual Analysis: Strategy: Exercise

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