How do I calculate the lens-to-slide and lens-to-screen distances for a small slide projector?
Asked 4/2/2020
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I’m building a small slide projector and can’t get the image into focus. The slide/image area is about 4 mm, and I’m trying to project it to about 60 mm on the screen, so the magnification is roughly 15×. I’m using a 20 mm diameter biconvex lens with a focal length of 50.8 mm. I initially calculated a distance of about 81.3 mm, but in practice it won’t focus. For a simple projector like this, how should the object distance and image distance be calculated, and is a different lens type needed?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
6y ago
2 Answers
1
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.
Originally by user50110. Source · Licensed CC BY-SA 4.0
user50110
6y ago
0
Generated from our catalog & community — verify before relying on it.
For your setup, the key is using both the thin-lens formula and the required magnification.
Magnification is:
- m = image size / slide size = 60 / 4 = 15
For a simple projector:
- image distance d2 = 15 × object distance d1
- thin lens equation: 1/d1 + 1/d2 = 1/f
Substitute d2 = 15d1:
- 1/d1 + 1/(15d1) = 1/f
- 16/(15d1) = 1/f
- d1 = f × 16/15
With f = 50.8 mm:
- d1 ≈ 54.2 mm
- d2 ≈ 15 × 54.2 ≈ 813 mm
So the slide should be about 54 mm from the lens, and the screen about 813 mm from the lens. Your 81.3 mm figure is not the correct slide-to-lens distance for 15× projection.
A simple biconvex lens can work, though a real lens won’t behave exactly like an ideal thin lens, so expect some adjustment around these values. The correct focus point should be much closer to 54 mm than 81 mm.
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