4:3 video via HDMI adapter to 4:3 projector -> video does not fill entire display

Hi,

I'm trying to display a 4:3 video from an iPad Air's default video player to a 4:3 projector which is connected via a lightning to HDMI adapter. Problem is, the video is "scaled" down on the projector's display, i.e. I have black bars all around. I can zoom this out so that the vertical bars vanish, but that results in a cropped image, i.e. the top and bottom bar remain.

Is that "expected" (I've found some indications that this might be caused by the HDMI adapter which always first goes to 16:9) or is there some solution to this? The thing is, for some reason this worked (fully 4:3, no black bars) about a year ago with a different video on an iPad 4 (older iOS version), same adapter and same projector...

cheers,

XCTrails