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Phy 133 - Assignment 3 A. 1. One ray reflects off a higher n, the other off a lower n. So, one gets a 180° phase shift, the other doesn’t. With no additional phase shift due to a path difference, the out of phase waves interfere destructively. 2. B. 1. Constructively: Path difference = a whole number of wavelengths. Destructively: Path difference = a whole number of wavelengths plus an extra half. (This is right on the formula sheet.) 2. C. 1. Oil’s n must be less than water’s. (and more than air’s.) If both rays reflect off a higher n, both undergo the same 180° phase shift. That way, interference is constructive when the thickness is nearly zero. 2. D. 1. From two lamps, the beams of light are not coherent. With one lamp, whatever is coming through one slit is coming through the other slit at the same time. With two, there is no relationship between the sources so there is no relationship between the waves arriving at a given point on the screen. Just a random jumble of phases everywhere. 2. E. His distance from the lower speaker is L, and his distance from the upper one is L2 42 . So the path difference for the two sounds is L2 16 L . There is a minimum whenever this equals (n + ½)λ. A) If you repeat the calculation with the path difference equal to 5λ/2 (or more) you will find the equation has no positive solution. The distances are assumed to be positive numbers here, so there just these two minima. F. Remember, the speed and wavelength of the light in water is not the same as in a vacuum. From n = λ= = , v= = = 2.249 x 108 m/s = 4.052 x 10-7 m Double slit maxima: mλ = d sinθ (2)(4.052 x 10-7) = (2.5 x 10-6)sinθ .3242 = sinθ θ = 18.9°