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Equation 6 · Part 7 · How Scientific Instruments and Metrology Actually Work

Numerator: 0.61λ

d  ≈  0.61 λnsin⁡αd \;\approx\; \frac{0.61\,\lambda}{n\sin\alpha}
0.61 λ0.61\,\lambda

What this part means

The complete quantity above the fraction bar.

Its job in the formula

0.61λ occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

An electron microscope is a useful worked example precisely because almost the entire modern instrument exists to correct for a limitation baked into its own optics. The achievable resolution of any imaging system with a circular aperture is bounded, in the simplest diffraction-limited approximation, by a form of the Rayleigh criterion: d  ≈  0.61 λnsin⁡αd \;\approx\; \frac{0.61\,\lambda}{n\sin\alpha}. 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…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the article section

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