 Electron optics

Electron optics studies how electric fields and magnetic fields guide electrons and form images. The Lorentz force supplies a trajectory description, while the de Broglie wavelength supplies the wave scale needed for diffraction. Both descriptions matter: steering a narrow beam and resolving two nearby specimen features are different achievements.

For a magnetic electron lens,Here $e>0$ is the elementary charge, $\mathbf{v}$ the electron velocity, and $\mathbf{B}$ the magnetic field. The second equality follows because a cross product is perpendicular to each factor: a static magnetic field bends the trajectory without increasing the kinetic energy. Acceleration instead requires work by an electric field. This distinction lets an electron microscope adjust imaging with magnetic fields while an accelerating voltage sets the electron momentum.

Electron optics is a field of study that focuses on the manipulation and control of electron beams using electromagnetic fields. It draws parallels with optical systems that handle visible light, but instead of light rays, it deals with trajectories of electrons, which are charged particles. This field is integral to the design and operation of various devices, such as electron microscopes, cathode ray tubes, and particle accelerators.