There are plenty of cheap projection clocks available, but as [Thomas Pototschnig] points out in this project, where’s the fun in just buying something? He set out to build a cheap projection clock using a small LCD screen, a cheap LED backlight, and a cheap lens. Cheap is the order of the day here, and [Thomas] succeeded admirably, creating a design that can be made with a couple of cheap PCBs, a 3D printer and the other parts mentioned above. He does a nice job of laying out his thinking in this design, showing how he calculated the projection path and made other decisions. His project has room to grow as well: it runs from an Arduino compatible STM32 that could handle many things other than showing the time if you were inclined to expand the project further.
[Thomas] has released all of the files he created for the project, including a number of options for the case that can use C-mount and Sony E-mount lenses. I’m not sure if you would want to attach your expensive camera lenses to a home-made projector like this, but it’s good to have the option if you have a dead E-mount lens that you were going to tear apart for parts anyway.