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I'm trying to build a small slide projector but (being a lens noob) I'm not able to get a proper focused image.

I'm trying to achieve this: Pinhole camera model description

I've got a 20mm (biconvex?) lens with a focal length of 50.8mm so when calculating the distance I would need a distance of about 81,28mm but whatever tweaking it does not focus.

Apparently I'm doing something wrong here or do I need a different type of lens?

Thanks in advance!

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Your drawing shows a projection magnification of 60/4 = 15x.

We can use this thin lens equation: 1/d1 + 1/d2 = 1/f together with d2 = (60/4) × d1 = 15 × d1 to get

15/d1 + 1/d1 = 15/f

16/d1 = 15/f

d1/16 = f/15

d1 = f × (16/15) or 54.19 mm.

For a realistic not-thin lens the distance from the center of the lens to the slide will not be exactly that, but assuming that your lens is fairly thin and small diameter it will be much closer to that than to 81.28 mm discussed in your question.

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