Question

A collimated beam of laser light is incident on a set of three lenses in air. The first lens is diverging (fi<0) while the second and third lenses are converging (f2>0, f;>0). The first and second lenses are separated by a distance d12, while the second and third lenses are separated by a distance d23. The system is designed to take the collimated beam of laser light expand it (lens 1), recollimate it (lens 2), and then focus it to a point (lens 3). Assuming all lenses can be considered thin, calculate expressions for the matrix elements a) (A,B,C,D) of the system matrix: b) Suppose you had numerical values for all of the focal lengths and distances. The distance from the final lens to a screen is d3s. How large should das be if the screen is to be at the focal plane of the system? Answer in terms of the general system matrix elements A,B,C, and D instead of the complicated expressions derived above. c) This optical system is a beam expander followed by an objective lens. Think about the wave nature of light and the size of the focal spot compared with the diameter of the collimated beam that is incident on the final lens. If two beams of diameters D1 and D2 are incident on a lens with D2>D1, which beam will have a smaller focal spot? A qualitative answer is sufficient. (Hint: To keep the matrix multiplications from becoming unmanageable try substituting in f12 for the combined focal length of lenses 1 and 2 together after performing your first three matrix multiplications.) Lens 1 Lens 2 Lens 3 d12 d35 dz3

Answer 1