[30] We are designing a car-mounted camera, and we will analyze its mount. The camera images objects onto the focal plane array (FPA), at a range as close as zo = -2 m. Optically, we will model the camera as a single thin lens, fixed with respect to the image plane, with the geometry shown in the diagram below. Assume paraxial rays and small angular errors. Mechanically, we will model the lens as a mass, and we will model the mount as a spring on one side and a hinge on the other side, as shown in the diagram below. Assume small angles and small deformations. Object + Zo Optical model Lens (Focal length f) Mechanical model L/2 A Zi k{ Tube Z Z 10x FPA Parameters: Stiffness: Mass of camera: FPA pixel size: Dimensions: f = 25 mm Zo [-2, -0) m L = 50 mm a = 5g (part d) k = 5N/m Mcam = 0.1 kg p = 5 m [5] What is the magnification of the optical system? [5] What is the sensitivity of image motion Ayim to rotation of the optical system 0, (lens plus image plane together)? This is not the same as if only the lens moves, since the FPA is moving as well. [10] What is the ratio of the angular deflection of the plate 0 for a force F applied at point A? [10] If the car creates a quasi-static acceleration a = 5g (g = 9.81 m/s) of the mount and optical system, what is the stiffness required to keep image motion less than 0.1 pixels on the FPA? If you can't solve part c, assume the ratios 0x