Help designing a mini slide projector

Question

After spending the better part of a year thinking about designing a tiny film projector I am beginning the process. I know the basics of photography but I find it very difficult to calculate what kinds of lenses I should use for such a unique application. I would be very grateful for any advice from this group. I am lucky to have found stack echange :)

My design idea:

• 5mm square picture made from 35mm positive film (I already have a prototype image)
• LED projector light
• Lenses to project the image from 1 to 5 meters away
• Cost is an issue so simple solutions would be preferable

If anyone can help me understand lens shape and positioning it would help me a lot.

Thanks!

Answer 1

It works exactly the opposite of photography: instead of picking a scene which is a metre wide a couple of metres away and projecting it on a 5mm sensor, you project the 5mm sensor to a one-metre wide image which is a couple of metres away. The two necessary equations are here. You can likely recycle an old camera lens. Enlarger lenses could also be a solution (they could be cheaper, attics are full of retired enlargers).

But your biggest problem is that the light that is projected goes through your slide, so to have a bright enough projected image you need to push enough lumens through your 25mm² slide which has an area that is 40000 times smaller than its one-meter projection. With incandescent light this requires a lot of cooling(*) even though a 24x36 slide has 35x the area of your slide. With LEDs this will also require some cooling, assuming you find a LED bright enough with such a small area. Otherwise you will have to use a larger led and focus is on the slide using another lens (or a suitably shaped reflector).

(*) Projections with incandescent light are also done on highly reflective screens to reduce the required lighting. Projecting in daylight on standard surface (white paint) and projecting in a dark room on a reflective screen have very different requirements.

Answer 2

About half of my 55+ years in the photo business, I worked in the photofinishing industry. The other half in the manufacture, sales and service of photofinishing equipment. Often, I needed to calculate, what focal length lens to use to make an enlargement from negative or slide, with a specified projection to a given magnification. First with pencil and paper and slide rule, followed by calculator, then computer.

Decide projection distance (slide/film to screen) call it D. Measure slide/film carrier, call it C. Settle on screen size, call it S. Calculate magnification, call it M All dimensions in millimeters Formula for focal length F: F=D/((M+1)^2/M)

Solve using 5mm slide film projected on screen 1000mm square distance 1000mm

Find M = S/M M = 1000 / 5 M= 200

M = 1000 / 5 = 200 D = 1000 S = 1000 M = 200

F = 1000/((200 +1)^2/200) F (focal length) = 4.95mm (use 5mm lens)

Example 2 2000mm projection distance F = 9.9mm (use 10mm lens)

Example 3 3000mm projection distance F = 14.85mm (use 15mm lens)

Example 4 4000mm projection distance F= 19.8mm (use 20mm lens)

Example 5 5000mm projection distance F= 24.75mm (use 25mm lens)