Optical spectrometers (often simply called "spectrometers"), in particular, show the intensity of light as a function of wavelength or of frequency. The deflection is produced either by refraction in a prism or by diffraction in a diffraction grating.
The energy spectrum of particles of known mass can also be measured by determining the time of flight between two detectors (and hence, the velocity) in a time-of-flight spectrometer. Alternatively, if the velocity is known, masses can be determined in a time-of-flight mass spectrometer.
When a fast charged particle (charge q, mass m) enters a constant magnetic field B at right angles, it is deflected into a circular path of radius r, due to the Lorentz force. The momentum p of the particle is then given by
where m and v are mass and velocity of the particle. The focussing principle of the oldest and simplest magnetic spectrometer, the semicircular spectrometer, invented by J. K. Danisz, is shown on the left. A constant magnetic field is perpendicular to the page. Charged particles of momentum p that pass the slit are deflected into circular paths of radius r = p/qB. It turns out that they all hit the horizontal line at nearly the same place, the focus; here a particle counter should be placed. Varying B, this makes possible to measure the energy spectrum of alpha particles in an alpha particle spectrometer, of beta particles in a beta particle spectrometer, of particles (e.g., fast ions) in a particle spectrometer, or to measure the relative content of the various masses in a mass spectrometer.
Since Danysz' time, many types of magnetic spectrometers more complicated than the semicircular type have been devised.
Generally, the resolution of an instrument tells us how well two close-lying energies (or wavelengths, or frequencies, or masses) can be resolved. Generally, for an instrument with mechanical slits, higher resolution will mean lower intensity.