If you are thinking of connecting your iPhone/iPad to a projector, I've got two ways for you. (Here I am using my projector - an AAXA M5- for the demonstration. But they should work for most of the models in the market.
HDMI Cable + Apple Lightning Digital AV Adapter
Due to iPhone’s always unique design, there is no AV Cable directly connecting a mini projector with an iPhone. But Apple created a particular Lightning Digital AV Adapter (Retail Price $49) to enable the mirroring of an iPhone (also iPad or iPod) screen to an HDMI-equipped TV, display, projector, or other compatible display in up to 1080p HD. It can also output video contents – movies, TV shows, and captured videos – to those big screens in up to 1080pHD. My projector doesn’t come with an HDMI cable, but it was easy to find it on Amazon (less than $10). After connecting the HDMI port (VIDEO IN) of the projector with iPhone through the cable and the adapter and choosing “DIGITAL INPUT” (or HDMI) on the Main Menu, you can start enjoying the large screen projections for you iPhone.
Lightning Presentation Cable
You can also find a Lightning Presentation Cable (about $30) to make the connectivity easier. This Lightning to HDMI Cable is capable of mirroring 1080p HD videos from an iPhone (as well as iPad) to the projector. To use this cable, just plug it in the Lightning port side to an iPhone, the HDMI side to the HDMI port of a projector and the USB port to an iPhone charger or the USB port on the projector.
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Many projectors have built-in WAPs, along with apps that allow one to use AppleTv or other wireless streaming/screen mirroring apps. For free, or nearly so.
Difference between these options and wired, besides price, is that the wired options are usually less (or not at all) compressed, and likely full framerate.