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1. Diffraction grating While rummaging around the optics lab one day, you find a small, flat piece of what looks like clear glass. Curiosity drives you to shine a Green laser (i=500 nm) through the plate in your quest to figure out what this plate is and why it's sitting in your lab. You observe a series of laser spots corning out of the plate at regularly spaced angles. The spots are separated by 10 cm when observed on a wall located 1 m away from the glass plate. Calculate the spacing of lines on the glass plate that would cause this pattern. 2. Diffraction-based measurement tool A graduate student at FIU AMERI needs to a quick measurement tool to assess the diameter and the shape of an aperture on a metallic substrate. The aperture is supposed to be perfectly round and its diameter = 10 um. Please design this measurement tool using the theory of diffraction. In your design, please specify (1) light source used, (2) types of measurements. 3. Ray optics Determine the ray-transfer matrix for an optical system made of 2 lenses separated by a distance d (shown below). The first lens is a compound lens, consisting of 1 biconvex lens and 1 biconcave lens (both of the same index of refraction). The second lens is biconvex. The focal length of all lenses share the same magnitude. (b) Please also describe the function of this lens system. Please note you may use thin lens approximation here. a I

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