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Unformatted text preview: Problems of the XV International Physics Olympiad (Sigtuna, 1984) Lars Gisln Department of Theoretical Physics, University of Lund, Sweden Theoretical problems Problem 1 a) Consider a planeparallel transparent plate, where the refractive index, n , varies with distance, z , from the lower surface (see figure). Show that = . The notation is that of the figure. n n n(z) A B z z = 0 b) Assume that you are standing in a large flat desert. At some distance you see what appears to be a water surface. When you approach the water is seems to move away such that the distance to the water is always constant. Explain the phenomenon. c) Compute the temperature of the air close to the ground in b) assuming that your eyes are located 1.60 m above the ground and that the distance to the water is 250 m. The refractive index of the air at 15 C and at normal air pressure (101.3 kPa) is 1.000276. The temperature of the air more than 1 m above the ground is assumed to be constant and equal to 30 C. The atmospheric pressure is assumed to be normal. The refractive index, n , is such that n 1 is proportional to the density of the air. Discuss the accuracy of your result. Solution: a) From the figure we get = 1 1 = 2 2 = = b) The phenomenon is due to total reflexion in a n A n B n n 1 2 a a a a 1 1 2 2 warm layer of air when = 90. This gives = c) As the density, , of the air is inversely proportional to the absolute temperature, T , for fixed pressure we have ( 29 = 1 + = 1+ / The value given at 15 C determines the value of k = 0.0795. In order to have total reflexion we have 30 = or 1 + 303 2 + 2 = 1 + with h = 1.6 m and L = 250 m As h << L we can use a power expansion in / : = 303 303 + 1 1 1+ 2 / 2 303 303 1+ 303 2 2 2 = 328 = 56 Problem 2 In certain lakes there is a strange phenomenon called seiching which is an oscillation of the water. Lakes in which you can see this water....
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This note was uploaded on 11/08/2011 for the course PHYS 0000 taught by Professor Na during the Spring '11 term at Rensselaer Polytechnic Institute.
 Spring '11
 NA
 Physics

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