Current submillisecond time-resolved broad-band infrared spectroscopy, one of the most frequently used techniques for studying structure-function relationships in life sciences, is typically limited to fast-cycling reactions that can be repeated thousands of times with high frequency. Notably, a majority of chemical and biological processes do not comply with this requirement. For example, the activation of vertebrate rhodopsin, a prototype of many protein receptors in biological organisms that mediate basic functions of life, including vision, smell, and taste, is irreversible. Here we present a dispersive single-shot Féry spectrometer setup that extends such spectroscopy to irreversible and slow-cycling systems by exploiting the unique properties of brilliant synchrotron infrared light combined with an advanced focal plane detector array embedded in a dispersive optical concept. We demonstrate our single-shot method on microbial actinorhodopsin with a slow photocycle and on vertebrate rhodopsin with irreversible activation.