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Hyperfocal distance
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====Definition 1==== An object at distance {{mvar|H}} forms a sharp image at distance {{mvar|x}} (blue line). Here, objects at infinity have images with a circle of confusion indicated by the brown ellipse where the upper red ray through the focal point intersects the blue line. First using similar triangles hatched in green, <math display="block">\begin{array}{crcl} & \dfrac{x-f}{c/2} & = & \dfrac{f}{D/2} \\ \therefore & x-f & = & \dfrac{cf}{D} \\ \therefore & x & = & f+\dfrac{cf}{D} \end{array}</math> Then using similar triangles dotted in purple, <math display="block">\begin{array}{crclcl} & \dfrac{H}{D/2} & = & \dfrac{x}{c/2} \\ \therefore & H & = & \dfrac{Dx}{c} & = & \dfrac{D}{c}\Big(f+\dfrac{cf}{D}\Big) \\ & & = & \dfrac{Df}{c}+f & = & \dfrac{f^2}{Nc}+f \end{array}</math> as found above.
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