Consider the paraxial layout of an optical system for a video microscope. In such a microscope, an objective lens is used to form an image directly onto a CCD detector (there is no eyepiece). The image is then viewed on a video monitor connected to the CCD. a) For a 5 mm focal length, 0.1 NAO, objective operating at an optical tube length of 200 mm determine the length of the system (from object to image) and the magnification of the system. b) Assume the microscope objective is diffraction limited. What is the smallest feature on the object that can be resolved with this microscope at 550 nm? c) Now find the maximum size of the sensor pixel that can be used if you want the resolution of the system at 550 nm to be limited by the objective and not the sensor. Note: this occurs when you have at least 2 sensors pixels "sampling" the Airy diffraction spot radius. d) If the Lagrange invariant of the system is equal to 0.1 mm what is the largest object that can be viewed with the system? What is the size of the sensor? e) If you decide to replace the CCD with a conventional 5x eyepiece what is the magnifying power of the microscope?