Power spectra (PS) of high-resolution images of M51 (NGC 5194) taken with the Hubble Space Telescope and the James Webb Space Telescope (JWST) have been examined for evidence of disk thickness in the form of a change in slope between large scales, which map two-dimensional correlated structures, and small scales, which map three-dimensional correlated structures. Such a slope change is observed here in Hα, and possibly Paα, using average PS of azimuthal intensity scans that avoid bright peaks. The physical scale of the slope change occurs at ∼120 pc and ∼170 pc for these two transitions, respectively. A radial dependence in the shape of the Hα PS also suggests that the length scale drops from ∼180 pc at 5 kpc, to ∼90 pc at 2 kpc, to ∼25 pc in the central ∼kpc. We interpret these lengths as comparable to the thicknesses of the star-forming disk traced by H ii regions. The corresponding emission measure is ∼100 times larger than what is expected from the diffuse ionized gas. The PS of JWST Mid-IR Instrument images in eight passbands have more gradual changes in slope, making it difficult to determine a specific value of the thickness for this emission.