Several times recently I have received calls or messages about projectors not displaying properly when connected to iMacs, or the iMac display changing when a projector is connected. The solution is to adjust the display settings so that the two displays "match" resolutions.
Although the iMacs are pretty good at automatically sensing a projector when it is connected, sometimes they do not do this properly or may not detect the projector at all if it is connected or disconnected with the Mac asleep.
1) On all of our school Macs you should see the Displays icon (looks like a monitor) in the menu bar (upper-right) in Finder. If your resolution has been reduced you may need to minimize/hide programs in order to see it. The first thing to try if you are not getting a correct image is to choose "detect displays" from this menu. This will force the Mac to check what is connected.
2) The second item in the Displays menu should say "mirroring on. " Mirroring means showing the same thing on screen and projector. Mirroring OFF will give you a spanned display: Think of an ultra-wide display showing across two monitors side-by-side, with the projector showing the right-hand monitor. There are times when this might be useful, like if you wanted to work on something on your screen while showing students a short video or website on the projector. If you ever see just your desktop background on the projector, it is likely that mirroring is off.
3) Sometimes connecting a projector will "dumb down" the iMac display, making everything larger or showing you a narrower screen. To fix this, start by changing “number of recent items” in the Displays menu to 5 (default is 3.) Next, scroll down the Displays menu to the lower section (iMac Display) and choose "1280 x 800." This is the point at which the two displays "match" and show a good image on both.
What makes this whole thing a challenge is that the proportions are different: our projectors are designed for 4:3 and the iMacs are 16:9. This is also why Windows computers do not have these issues, since they are designed for 4:3 display.