Gradient index lenses were formed in a liquid-filled cavity supporting an ultrasonic standing wave. The constructed devices acted as diverging lenses or axicon lenses, depending on whether the center or edge region is interrogated. The focal length of the diverging lens was controllable with the frequency and amplitude of applied ultrasound from −100 mm to negative infinity. Experiments and models suggest that the primary process contributing to lensing is the steady-state density component of the finite-amplitude standing wave; sound amplitudes up to 150 MPa were calculated in glycerin, corresponding to a maximum contrast in the refractive on the order of 0.1%. This amplitude was also sufficient to move high index nanometer-scale particles via an acoustic radiation force and thereby create larger refractive index gradients. The segregation of suspended nanoparticles was found to enhance the lensing effects that occurred in the pure fluids. Concepts are also explored to manipulate the particle distribution in order to create converging lenses and/or other desirable optical components.