I got a rather nice Victorian magic lantern projector in a car boot sale. It's probably a "Walter Tyler Helioscopic Magic Lantern" from around 1890.
Like many such lanterns, it had lost its oil-lamp burner so I decided to give it an LED lamp.
It still has the reflector attached to a brass arm so I could use that to support the LED. The reflector could also act as part of the heat-sink for the LED.
(As with all such "modernisations", one should not make changes to the original antique.)
Step 1: What Kind of LED?
My first thought was to use a flat COB LED to give even illumination. I bought:
(Or search eBay for "48 LED COB 8W".)
It's easy to install - it has a sticky back - and can be connected straight to 12V. I could stick it onto a sheet of metal but it didn't seem to need much of a heatsink.
The projector has a condenser between the "lamp" and the slide so the divergent light from the COB LED was focussed in the slide.
Unfortunately, I couldn't get a sharp image. That really surprised me. Surely all that matters for focus is that the slide is in the right place? The illumination might affect the brightness but not the focus. I knew you needed a focussed condenser for microscopy but why did it matter for a projector? The web suggested that a projector's condenser was needed for even, bright illumination but not for focus. Did I need a "point source"? Weird.
Step 2: Point Source LED
So I got a small 3W LED.
(Or search eBay for "10PCS 3W High Power Led".)
The forward voltage of the LED is around 3V. For 3W that implies a current of around 1A. To reduce the heat generated I chose a 5V power supply and, to extend its life, I decided to use a current of around 0.5A. so that's
(5V - 3V) / 0.5A = 4ohm
0.5A * 0.5A * 4ohm = 1W
So I needed a 4ohm 1W resistor.
(The actual forward voltage varied between 2.5V and 3.5V depending on the current.)
I wired it up and held it inside the projector and got a much crisper image. Really weird.
Step 3: Installing the LED
I made the LED holder out of tinplate. It clips over the reflector and acts as a heatsink. Tinplate seemed to be in keeping with the rest of the projector. I have lots of tinplate from old cans of dried milk - it's easy to soft-solder and is a very useful material for prototyping.
The LED has a flat disk on its back which should be soldered to a heatsink. It also has two terminals which are at the same height as the flat disk. (One is marked with a "-" sign and is connected to the negative of the supply.)
Clearly you need to raise the back of the LED off the plate so the terminals don't touch it. Balance the plate over the open jaws of a vice and tap a flat piece of steel against it, creating a "platform". A nut is an ideal tool. One tap is enough.
Tin the back of the LED and both the front and back of the "platform". Hold the LED on the front of the platform and heat the back of the platform with a soldering iron that has a large bit. If your soldering iron isn't big enough, use a small blowtorch. If you don't have a blowtorch, try a gas barbecue lighter from a "dollar store" - they produce a small hot blue flame and are useful for this kind of work.
The tinplate is curved to fit the reflector and the corners have tabs which hook over it. One of the tabs is extended and wraps around the resistor to act as a heatsink.
The total heat dissipated is around 3W. 1W from the resistor and 2W from the LED (assuming the LED is 30% efficient). The tinplate gets sbout as hot as holding a hot cup of coffee - that's 80°C. It would be better practice to run the LED at a lower temperature so it's not going to last 50 000 hrs. But this is a magic lantern so its expected usage is more like a hundred hours.
Step 4: Power Supply
The power supply is a 5V "wall wart" from a charity shop or car boot sale. They're so cheap, reliable and widely available that they're not worth buying new. The label says 5V 1.5A and it has a "power jack" connector. Choose a switching power supply for reliability (they weigh less that the transformer kind). Don't choose a "phone charger" with a weird plug and a low current.
Buy a matching power jack socket. Measure the outer diameter of the plug - mine is 3.5mm - and search eBay for a matching socket, e.g. "power jack socket 3.5mm". The diameter of the pin in the socket is often specified as well (i.e. the diameter of the hole in the plug) for instance "3.5mm x 1.3mm".
I embedded the jack socket in a block of wood. (Actually MDF.) I drilled part way through to make a cavity for the socket and another hole all the way through so the block fits on the brass post of the reflector. I painted it black to look in keeping with the projector.
It works well. It's bright and reliable. Heat builds up inside the projector but nowhere near what it must have been like with an old oil burner.