a) [5] What is the sensitivity of tilt angle x (rotation about the x-axis) to adjuster screw rotations screw1 (rotation of adjuster screw 1 about its central axis)? Assume x is a small angle. b) [5] The magnification of the secondary mirror is m = -3 and tilting the mirror by Ox is equivalent to a decenter of Ay = fix. Assuming the mirror behaves like a thin lens, and the object (at z = f) does not move, what is the sensitivity of image motion to mirror tilt x? c) [15] For a preload force Fp = 100 N and gravity oriented along the +z axis, what is the force on each adjuster screw (1,2,3)? Ignore the mass of the stage. d) [5] What is the minimum preload force Fp required in each spring to avoid loss of contact between the mirror mount plate and the base? If you can't solve part c, state the condition(s) for loss of contact. [30] We will analyze the secondary mirror mount of a Gregorian telescope, shown below. The mirror mount has two main components: (i) a base that is fixed to the telescope structure and contains three adjuster screws, and (ii) a mirror mount plate which can tilt about the x- and y-axes and translate along the z-axis by turning the adjuster screws. The two components are held together with preload springs, which are pre-stretched, and each apply a tensile preload Fp to each component. The diagram shows all relevant dimensions and properties. Adjuster. screw 1 location 82 a a ^Z 1 screw1 x 2012 Z y -Preload spring locations (2X) 3 Tensioned preload spring (2X) Mirror mount plate Mirror mount plate (base not shown) Screw pitch: Mirror focal length 1: -Adjuster screw (3X) Mirror focal length 2: Mirror magnification: Mirror mass: Base (fixed to telescope structure) y Mirror -f- Dimensions a = 100 mm f Object Image p = 0.1 mm f= 500 mm f = 1500 mm m = -3 Msec = 5 kg 'N