What is the primary purpose of the spectrograph when attached to an optical or radio telescope?

To determine an object's chemical composition and speed by analyzing its spectrum

The spectrograph, although classified as an attachment rather than the main light collector, is one of the most vital tools in modern astronomy. Its fundamental operation involves separating the incoming light collected by the primary telescope (whether optical or radio) into its constituent component wavelengths, similar to how a prism creates a rainbow. By meticulously analyzing this resulting spectrum—looking at the position, width, and intensity of the spectral lines—astronomers can deduce a vast amount of physical data about the celestial source. This analysis reveals the object's chemical makeup, its temperature, and its relative velocity toward or away from Earth via the Doppler shift.