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m →The Rayleigh criterion: This is using small-angle approximation |
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Considering diffraction through a circular aperture, this translates into:
:<math> \theta\approx 1.22 \frac{\lambda}{D}\quad(\text{considering that}\,\sin\theta\approx\theta)</math>
where ''θ'' is the ''angular resolution'' ([[radians]]), ''λ'' is the [[wavelength]] of light, and ''D'' is the [[diameter]] of the lens' aperture. The factor 1.22 is derived from a calculation of the position of the first dark circular ring surrounding the central [[Airy disc]] of the [[diffraction]] pattern. This number is more precisely 1.21966989... ({{OEIS2C|A245461}}), the first zero of the order-one [[Bessel function of the first kind]] <math>J_{1}(x)</math> divided by [[pi|π]].
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