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Problem 2 Density Proles and Desert Mirages A necessary condition for the formation of a mirage is that the density of the air increases with increasing height (if > 0). Show that this condition is realized if the decrease of atmospheric temperature with height is n times greater than the dry adiabatic lapse rate (g > nfd). Determine the value of n. [Hint Take the natural logarithm of both sides of the ideal gas equation and then differentiate with respect to height. Combine with the hydrostatic equation and proceed to the solution] [20 points]