To enable extension of a zoom range at a maximum depending on a mode, in a projection device or an imaging device.

In setting the mode from a plurality of modes with different image heights, a zoom range is set so as to be extended in a mode where the image height becomes small. In a projection device, the zoom range can be extended for, for example, a vertically-long screen, a wide screen, and at trapezoid correction. In an imaging device, the zoom range can be extended for vertically-long photographing, panoramic photographing, and at digital zoom setting.