C using the results from above why do we see a

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Unformatted text preview: nteger multiple of 2π . |φAB − φACD | = 2πN . (a) Write an expression for the phase difference in terms of Θi , n1 , n2 , d, and λ0 . (b) If the oil film is 1 µm thick, at what angles do we see the first strong reflections for λ = 450nm, λ = 530nm, and λ = 630nm? (c) Using the results from above, why do we see a rainbow of colors on an oil slick? (d) For TM polarized light, what happens when the angle for constructive interference is equal to Brewster’s Angle for the air-oil interface? 4 6.007 Spring 2011 Problem Set 8: Electromagnetic Waves at Boundaries Problem 8.4 – Rainbows A very narrow beam of unpolarized red light of intensity Io is incident (at A) on a spherical water drop (see figure above). At A, some of the light is reflected and some enters the water drop. The refracted light reaches the surface of the drop at B where some of the light is reflected back into the water, and some emerges into the air. The light that is reflected back into the water reaches the surface of the drop at C where some of the light is reflected back into the drop, and some emerges into the air. The index of refraction of water for the red light is nred =1.331. (a) Using the data form the figure, what is the angle α? (You can leave this answer in the form of an expression.) (b) What is the intensity of light that refracts into the drop at A? (Take into account both TE and TM polarized light.) (c) For what value of angle would you find that the light reflected at A is entirely TE polarized ? (You can leave this answer in the form of an expression.) (d) What is the dominant polarization of light that emerges at B? Explain. 5 6.007 Spring 2011 Problem Set 8: Electromagnetic Waves at Boundaries (e) For blue light, the index of refraction in water is 1.343. The speed of blue light in water is therefore about 1% slower than that of red light. In the figure above, showing the red-light path, assume that the incoming narrow beam of light also contains blue-light and draw the trajectory that the blue-light beam would take after it enters the water droplet at A. (f) If you look at the rainbow in the sky you will notice that the blue band of color is closest to the ground and the red color band is highest up. Using the figure below explain why the colors are ordered in this manner. 6...
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