We measured the reflectivity of the multifold semimetal RhSi in a frequency range from 80 to 20000 cm$^{-1}$ (10 meV - 2.5 eV) at temperatures down to 10 K. The optical conductivity, calculated from the reflectivity, is dominated by the free-carrier (Drude) contribution below 1000 cm$^{-1}$ (120 meV) and by interband transitions at higher frequencies. The temperature-induced changes in the spectra are generally weak: only the Drude bands narrow upon cooling, with an unscreened plasma frequency that is constant with temperature at approximately 1.4 eV, in agreement with a weak temperature dependence of the free-carrier concentration determined by Hall measurements. The interband portion of conductivity exhibits two linear-in-frequency regions below 5000 cm$^{-1}$ ($sim$ 600 meV), a broad flat maximum at around 6000 cm$^{-1}$ (750 meV), and a further increase starting around 10000 cm$^{-1}$ ($sim$ 1.2 eV). We assign the linear behavior of the interband conductivity to transitions between the linear bands near the band crossing points. Our findings are in accord with the predictions for the low-energy conductivity behavior in multifold semimetals and with earlier computations based on band structure calculations for RhSi.
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