We have measured angle-dependent photoemission spectra for one-photon and two-photon excitation from Ag(111). The observed dispersion of the sp-band transition of Ag(111) can be reproduced using a nearly-free-electron model for the initial and final states involved. The observed dispersion agrees with the known band structure. We illustrate how the strong refraction of low-energy electrons becomes a limiting factor to obtain quantitative band-structure information. Conversely, low-energy electrons of a well-defined direct optical interband transition can provide a sensitive probe of the inner potential. We observe asymmetric two-photon photoelectron intensity distributions with respect to detection along the surface normal. These intensity distributions can be well described by a phenomenological model which employs the Fresnel equations to calculate the electric field components of the incident radiation inside the sample. Very good agreement is found using tabulated optical constants and a momentum matrix element, which is oriented along the surface normal. In contrast, the observed intensity distribution for one-photon photoemission from Ag(111) does not fit the simple Fresnel model. We interpret this as the influence of surface photoemission. By comparison to Cu(001), we show that the expected intensity distributions of the Fresnel model for one-photon photoemission and two-photon photoemission are valid for an orientation of the momentum matrix element along the surface normal if the influence of additional effects like surface photoemission can be neglected.