← Back to article

Equation 8 · How Scientific Instruments and Metrology Actually Work

What does this equation mean?

nsin⁡αn\sin\alpha

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

nn

Symbol n

n is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Understand this part →

α\alpha

Symbol α

the numerical aperture of the imaging system.

Understand this part →

How to interpret it

Read this expression with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

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.

Read the equation in its article →

Sources cited in the article section

These citations give research context. Read each source to check which claims it supports.

Return to How Scientific Instruments and Metrology Actually Work

See this formula across 1 published context →

Browse the mathematical compendium →