Correct Image Resolutions for Images in Screens

Hello -

I am building a site using Screens and have full screen images as the background for all of my screens. I am wanting the background image to properly display full screen on desktop/tablet and mobile b/c Screens allows images for both desktop/tablet and mobile. I am assuming that the largest full screen size I would realistically need to account for for desktop would be the iMac 27" Retina 5k. The resolution for this screen is 5120 by 2880 pixels. However, b/c this is Retina I am not clear on what the proper image resolution should be to accommodate this screen.

For mobile, I am assuming that the largest screen I would need to account for would be the iPhone 6s Plus with a 1920-by-1080-pixel resolution. However, again I am not clear on what the proper image resolution should be to accommodate the retina display.

I would love advice on this. I have Google’d this and have not found clear information. Also, if my assumptions above are incorrect, please illuminate me.

Much appreciated!

Lion