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Blinky Boxes
Alright, so you wanna throw your precious device onto the big screen? Cool story. You're gonna need some extra gear. Here's the tea:
AirPlay
Beam your iOS device's video content to an HDTV or projector like you're some kinda wireless wizard. Psych — you need an AppleTV plugged into your HDTV & a WiFi connection that actually works. (Internet? Nah, we don't need no stinkin' internet for this one.)
Digital A/V Adapter
Wanna go old school & plug stuff in with cables like it's 1997? Hook your device directly to any video output that has HDMI. Apple sells the adapter (of course they do). Third-party adapters? Lol, iOS said "nope, fam."
VGA Adapter
Got a dusty old projector from the Stone Age? VGA is your sad, analog friend. Grab the right adapter for your device & pretend it's retro-chic.
Note: Devices older than the first-gen iPad basically can't talk to external video stuff at all. & yeah, that first-gen iPad? It's too cool for AirPlay video. (Spoiler: it's not cool.)