6. An optical coating system uses a thin film thickness monitor to measure the thickness of an evaporated material that is deposited onto one side of a substrate. One such instrument uses a 2.00-cm diameter quartz crystal disk that is made to oscillate at a particular frequency. As the crystal gets (uniformly) coated on the circular area facing the source of evaporated material, the initial frequency fo of the crystal shifts due to the mass of the coating deposited onto it. This system may be modeled as a spring-mass system. (a) Derive an equation for the shift (or change) in frequency of the crystal (of mass mcrystal) as material (of mass mcoating) gets deposited on it. (b) Given that the mass of the quartz disk is 0.416 g, and it is made to oscillate initially at 5.00 MHz, what will be the shift (or change) in frequency of the crystal after it is coated with a layer of magnesium fluoride (p= 3.15 g/cm)) that is 138 nm thick? Substrate Thermal evaporation Evaporated atom from source Degassing from the heated connections Source