This is called biasing the mach zehnder e consider

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Unformatted text preview: n that you would choose to start with? This is called biasing the Mach-Zehnder (e) Consider the same sensing configuration as part (d) but the first semitransparent mirror is not perfect and splits the light beams in a ratio of 40:60 instead of 50:50, with less intensity passing through the container with sugar. What are the expressions now for the E fields and of Iout ? With the same biasing condition as before, does this increase or decrease your sensitivity? (f ) Now you have the choice of using either a light source of 633 nm or 800 nm to perform the intensity measurements described above. Which wavelength would you use to have the best sensitivity? Problem 7.5 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. 6 6.007 Spring 2011 Problem Set 7 (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. 7...
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