To provide a back light device high in the use efficiency of light not only when the device is used as a back light but when it is used as a reflector.

A reflection polarizing plate 14 is disposed on the back face side of a liquid crystal display element 1, and a liquid crystal cell 21 for polarization conversion is disposed between a light guide member 15 and a reflecting plate 17 disposed in the back side of the reflection polarizing plate 14. The cell 21 can be switched according to application of voltage between the aligned state of liquid crystal molecules which generates phase difference corresponding to 1/4 wavelength in the transmitted light to change the polarizing state and the aligned state of the liquid crystal molecules which does not generate phase difference for the transmitted light. Therefore, the liquid crystal cell 21 for polarization conversion can be used as a 1/4λ plate or can be used as a light- transmitting member generating no phase difference.