Reconfigurable intelligent surfaces (RISs) provide an interface between the electromagnetic world of wireless propagation environments and the digital world of information science. Simple yet sufficiently accurate path loss models for RISs are an important basis for theoretical analysis and optimization of RIS-assisted wireless communication systems. In this paper, we refine our previously proposed free-space path loss model for RISs to make it simpler, more applicable, and easier to use. The impact of the antenna's directivity of the transmitter, receiver, and the unit cells of the RIS on the path loss is explicitly formulated as an angle-dependent loss factor. The refined model gives more accurate estimates of the path loss of RISs comprised of unit cells with a deep sub-wavelength size. Based on the proposed model, the properties of a single unit cell are evaluated in terms of scattering performance, power consumption, and area, which allows us to unveil fundamental considerations for deploying RISs in high frequency bands. Two fabricated RISs operating in the millimeter-wave (mmWave) band are utilized to carry out a measurement campaign. The measurement results are shown to be in good agreement with the proposed path loss model. In addition, the experimental results suggest an effective form to characterize the power radiation pattern of the unit cell for path loss modeling.