To provide a liquid crystal optical element for controlling the angle of refraction of the rays of light to be transmitted by changing a voltage to be applied.

An optical deflection liquid crystal cell 100 includes: a pair of mutually opposed first and second transparent substrates; a pair of first and second transparent electrodes formed on the first and second transparent substrates, which applies a voltage between the first and second transparent substrates; a prism layer having a prism formed on the upper part of one of the first and second transparent substrates; an orientation film formed on the prism layer, which has been subjected to orientation processing in parallel with the direction of polarization of the polarizing plate of a liquid crystal display device 22; and a liquid crystal layer interposed between the first and second transparent substrates, which has liquid crystal molecules. A control part 28 controls the angle of refraction of the rays of light which pass through an interface between the slope of the prism and the liquid crystal layer by changing the refractivity of the liquid crystal layer by changing a voltage to be applied to the first and second transparent electrodes according to information from the outside.