We predict quantized Imbert-Fedorov, Goos-Hänchen, and photonic spin Hall shifts for light beams impinging on a graphene-on-substrate system in an external magnetic field. In the quantum Hall regime the Imbert-Fedorov and photonic spin Hall shifts are quantized in integer multiples of the fine structure constant α, while the GoosHänchen ones in multiples of α 2 . We investigate the influence on these shifts of magnetic field, temperature, and material dispersion and dissipation. An experimental demonstration of quantized beam shifts could be achieved at terahertz frequencies for moderate values of the magnetic field.Reflection and refraction of light are among the most common phenomena in optics. For a plane wave impinging on an interface separating two media, the propagation of the reflected and transmitted waves is governed by the Fresnel and Snell laws [1]. However, this standard geometric optics picture does not apply for a beam of finite width consisting of the superposition of several plane wave components. In this case spatial and angular deviations from the expected ray trajectories occur, resulting in beam shifts within and transverse to the incidence plane, respectively called Goos-Hänchen (GH) [2] and Imbert-Fedorov (IF) [3,4] shifts. Even though the spatial IF shift vanishes for transverse electric or transverse magnetic linearly polarized light, photons with opposite heliticities are still shifted to distinct edges of the reflected/transmitted beam cross section -the spin Hall effect of light (SHEL) [5][6][7][8][9]. These shifts are relevant for biosensing [10] and nano-probing [11], and have been studied for a variety of beam profiles and material media [12][13][14][15][16][17][18][19][20][21]. In particular, the influence of gated graphene on beam shifts has been recently investigated [22][23][24], and a giant spatial GH shift has been measured [25].Here, we show that the magneto-optical response of a graphene-on-substrate system in the presence of an external magnetic field strongly affects beam shifts. In the quantum Hall regime characterized by well-resolved Landau levels in graphene, the IF and SHEL shifts are quantized in integer multiple of the fine structure constant α = e 2 /4πε 0 c, while the GH shifts are quantized in integer multiples of α 2 . Disorder broadening of inter-level transitions results in the IF, GH, and SHEL shifts to exhibit a discontinuous behavior at moderate magnetic fields reflecting the discrete Landau-level filling factor. Furthermore, due to time-reversal symmetry breaking, for linearly-polarized incident light the IF shifts change sign when the direction of the applied magnetic field is reversed, while the other shifts remain unchanged. Finally, we discuss the effects of temperature, dispersion, and the role of the substrate in this problem.Let us consider a monochromatic (frequency ω) Gaussian wave-packet propagating in air and impinging at an angle θ on a non-magnetic, isotropic, and homogeneous substrate of permittivity ε. A graphene sheet is placed on top of ...