An optical system may include equipment with a housing that is configured to receive external equipment such as a cellular telephone. The external equipment may include a display. To control the persistence of the display, the optical system may include a light modulating layer. The light modulating layer may switch between a transparent state in which display image light is passed through the light modulating layer to reach the viewer and an opaque state in which display image light is blocked by the light modulating layer from reaching the viewer. The light modulating layer may be placed in the transparent state for a portion of each display frame and the opaque state for the remaining portion of each display frame. The light modulating layer may be formed in the housing of the equipment that receives the external equipment or may be formed with the external equipment directly.