A common application of plano-concave cylindrical lenses is shown to the right. A collimated laser beam of radius r0 is incident upon a cylindrical plano-concave lens of focal length -f. In this figure, the radius of the laser beam is exaggerated for clarity. The laser beam will expand with a half-angle θ of r0/f. The laser beam will appear to be expanding from a virtual source placed a distance f behind the lens. At a distance z after the lens, there will be a line with thickness 2r0 (ignoring expansion of the Gaussian beam) and length L = 2 (r0/f)(z+f). If z is large compared to f, then we have an expansion ratio that is very close to z/f. This is not an imaging problem; we are projecting the laser beam into a line at a particular distance. The length of the line is simply proportional to z.
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A common application of plano-concave cylindrical lenses is shown to the right. A collimated laser beam of radius r0 is incident upon a cylindrical plano-concave lens of focal length -f. In this figure, the radius of the laser beam is exaggerated for clarity. The laser beam will expand with a half-angle θ of r0/f. The laser beam will appear to be expanding from a virtual source placed a distance f behind the lens. At a distance z after the lens, there will be a line with thickness 2r0 (ignoring expansion of the Gaussian beam) and length L = 2 (r0/f)(z+f). If z is large compared to f, then we have an expansion ratio that is very close to z/f. This is not an imaging problem; we are projecting the laser beam into a line at a particular distance. The length of the line is simply proportional to z.
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