[15] If there were no preload force, what would be the change in gap between the stack of lenses and the mount, per unit temperature, Ag/AT? You may assume all lenses remain in contact, except for a small gap between lens 1 and the retaining ring. [10] What is the change in force (in the contact annuli) per unit change in temperature, AF /AT? Specify whether the compressive preload force increases or decreases in magnitude with increasing temperature. [5] If the system is assembled at To = 25 C and its temperature drops to 1 = -50 Cat altitude, what is the preload force required to avoid loss of contact, and keep the total magnitude force in the contacts less than 1000 N (compressive)? Only one or the other requirements is relevant for this change in temperature. [10] The total allowable RMS wavefront error that is introduced by lens element surface height error is 0.50 um. What is the allowable RMS surface height error on each surface? Assume: (i) each lens aperture is filled, (ii) all angles of incidence are zero, (iii) the refractive index of all lens elements is 1.50 and the refractive index of the surrounding medium is 1, and (iv) the surface height errors are random (normally distributed) and uncorrelated with one another.[40] We are designing a lens tube for use in a high-altitude balloon. The tube contains two lens elements and one spacer held in place with a retaining ring, as shown below. There is a compressive preload force Fo generated by tightening the retaining ring, and all interfaces between components can only push- not pull-on each other. The relevant stiffnesses are included below, and any stiffness value not listed can be assumed to be infinity. Assume thermal soak conditions. Cross section of a lens cell Stiffnesses (Force along z, deformation along z): All annular contacts: Kc = 25 N/ um Lens 1: KL1 = 10,000 N/um b Spacer: ks = 50 N/um Lens 2: KL2 = 5,000 N/um Coefficients of thermal expansion: Tube: aT = 8 ppm/K Retaining ring Lens 1: all = 3 ppm/K Spacer: as = 24 ppm/K Lens 2: Lens 1 al2 = 8 ppm/K Dimensions: Z a = 5 mm Spacer - b = 60 mm Lens 2 c = 10 mm Tube