Lens device that includes converging lens having light output surface being spaced apart along lens axis from light input surface. Converging lens has total internal reflection side surface being spaced apart around lens axis and having frusto-conical shape extending between light input and output surfaces of the converging lens. Portion of light input surface of converging lens includes light input cavity being bounded by perimeter and having central axis and being generally shaped as portion of spheroid. Light input cavity has plurality of grooves each respectively following spline along light input surface that intersects with central axis of light input cavity and with respective point on perimeter, wherein each of respective points are mutually spaced apart around perimeter of light input cavity. Lighting system including lens device.