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nsin⁡αn\sin\alpha

Why this formula appears here

where λ\lambda is the wavelength of the illuminating radiation, and nsin⁡\sinα\alpha is the numerical aperture of the imaging system. For visible light this caps optical microscopy at roughly 200 nanometres — far too coarse to resolve individual atoms, whose spacing in a solid is typically a few tenths of a nanometre. Electron microscopy exploits the far shorter de Broglie wavelength of accelerated electrons — picometre scale at typical accelerating voltages — to push the diffraction limit itself down by more than three orders of magnitude.

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nsin⁡αn\sin\alpha

Equation 8 · Scientific Methods

How Scientific Instruments and Metrology Actually Work

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

where λ\lambda is the wavelength of the illuminating radiation, and nsin⁡\sinα\alpha is the numerical aperture of the imaging system. For visible light this caps optical microscopy at roughly 200 nanometres — far too coarse to resolve individual atoms, whose spacing in a solid is typically a few tenths of a nanometre. Electron microscopy exploits the far shorter de Broglie wavelength of accelerated electrons — picometre scale at typical accelerating voltages — to push the diffraction limit itself down by more than three orders of magnitude.

Meanings in this article

  • α\alpha: the numerical aperture of the imaging system.
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