How does Titanium dioxide reflect visible and IR lights?

TiO2 has an extremely high index of refraction. So for a broad range of angles of incidence of a light beam (consisting of a mix of frequencies) onto a TiO2 crystal face, almost all the light will be reflected off it. So if you crush up TiO2 into a powder consisting of many, many tiny crystallites of TiO2 with their crystal facets randomly oriented, almost all the different colors of incident light get reflected (or scattered) off the powder in random directions and the powder looks perfectly white.