Problem 2 Density Profiles and Desert Mirages A necessary condition for the formation of a mirage is that the density of the air increases with increasing height (de > 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 (->na). 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]