Half mirror and mirror with image display function

Provided are: a mirror with an image display function with which it is possible to observe a display image and a mirror reflection image without directional dependency even through polarized sunglasses, and with which a bright image display with good color is possible; and a half mirror that allows an image display device with a mirror function to be implemented. The half mirror includes, in the stated order, a phase differential layer, a circular polarized light reflection layer, and a front-surface plate, the front surface phase differential of the phase differential layer at a measurement wavelength of 500 m being 107-127 nm and the front surface phase differential at a measurement wavelength of 475 m being 110-130 nm, the circular polarized light reflection layer including three cholesteric liquid-crystal layers, the three cholesteric liquid-crystal layers each having central wavelengths λ1, λ2, λ3 of mutually differing selective reflection, the central wavelengths λ1, λ2, λ3 satisfying the conditions 380 nm < λ1 < 500 nm and 520 nm < λ2 < λ3 < 780 nm, and the cholesteric liquid-crystal layer that has the central wavelength λ1 being closest to the front-surface plate.