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An optical microscope uses visible light to magnify the image of a sample. Light interacts with the sample, and the objective lens collects the scattered light, forming an enlarged image that can be viewed by the observer.

Both light and electrons exhibit wave behaviors as described by classical and quantum mechanics. This wave behavior is crucial for understanding how electrons can be used in microscopy. In classical mechanics, the wavelength of light is what limits the resolution of an optical microscope. In quantum mechanics, electrons also display wave-like properties, described by the wavefunction. According to the de Broglie relation, the wavelength (\(λ\)) of an electron is inversely proportional to its momentum (\(p\)): \( λ = \frac{h}{p} \), where \(h\) is the Planck constant.

The wavelength of visible light (\(λ\)) is between 400 nm and 700 nm. However, the wavelength of an electron (\(λ_e\)) at high energy (such as those used in an electron microscope) is much shorter in comparison. The shorter the wavelength, the better the resolution and the smaller the details that can be observed. Because electron wavelengths are much shorter than visible light wavelengths, electron microscopes provide a much higher resolution than optical microscopes.

An electron microscope generates a beam of electrons that interacts with the sample, similar to how light interacts with the sample in an optical microscope. The scattered electrons are then collected by a magnetic lens, which forms a magnified image of the sample. Due to the shorter wavelengths of the electrons, electron microscopy can achieve resolutions that are orders of magnitude better than those obtained with light, allowing for the detailed study of tiny structures, such as atoms and molecules. In conclusion, electrons play the role that light does in optical microscopes for electron microscopes because they also exhibit wave behaviors. The shorter wavelengths of electrons allow electron microscopes to achieve a much higher resolution than optical microscopes, making it possible to study structures at the atomic scale.