# Projecting an image back into a slide projector

1. Apr 18, 2014

### LuukS

Hello,

I am working on a project in which I want to project a projection back into a slide projector using a concave mirror.

The lens of the projector has a focal point of 100mm (and an aperture of 2.8) and I want to have approximately 1 meter space between the mirror and the projector. Unfortunately I am not sure what the curvature or focal point of the mirror should be.

I tried to calculate this using the lens formula:

(From slide projector to projection, focused 2 meters away)
1/o + 1/i = 1/f
f = 100mm
i = 2000mm (to the mirror and back is 2 meters)
o = 105mm (distance between the slide and the lens)

(from the mirror back to the slide projector)

1/o + 1/i = 1/f
f = ?
i = 1000mm (image needs to be projected 1 meter back)
o = 1000mm ('object' is 1 meter behind the mirror)

That makes f = 500mm, meaning that the focal point of the mirror should be half of the distance between the mirror and the projector.

I am not sure if I am doing this correctly though... does anyone have any suggestions?

Thank you very much!

2. Apr 18, 2014

### Simon Bridge

Where do you want the image to be?

3. Apr 19, 2014

### LuukS

Inside of the projector.. So basically I want to project the image back onto the lens. The image doesn't have to be visible and I am ok with the risk of overheating the projector.

4. Apr 19, 2014

### Simon Bridge

Yes but where inside the projector?

Note:
1. projectors usually have a compound lens that you can adjust to sharpen the image.
2. to see an image in a mirror, the object cannot be at the same position as the mirror - you can use an image from one optical component as the object for another one to work out the effect of a combination of them. This also means that projecting an image "onto the lens" will not produce an image for the combined system.

In the projector:
The slide is the object - it is some distance one side of the lens, the lens puts a real image on the screen some distance away. This image is used as the object for the mirror ... which you will want to cast a real-inverted image back to some position that the lens will be able to use as an object in turn.

You need to know where you want the final image to end up to get the chain of image/objects to work out.

Last edited: Apr 19, 2014
5. Apr 19, 2014

### dauto

All you need to do is make sure that the projector is at the center of the mirror (The radius of the mirror is twice is focal distance. The image will form exactly over the original object. Why do you want to do that?

6. Apr 19, 2014

### LuukS

I think I should be a little bit more clear: It is going to be an artwork, in which people are probably not going to be able to see the image. Therefore there doesn't really have to be a sharp image anywhere inside of the projector, as long as all the light that comes out of the projector is reflected back into it. So I thought that it would be sufficient to reflect the projection right back onto the lens (and not worry about what happens with it inside of the projector).
I think that the image on the screen which is used as an object for the mirror is then the last object in the chain.

Regarding the lens, I might want to focus the lens in such a way that if someone puts his hand in between the mirror and the projector they can see a relatively sharp image.

7. Apr 19, 2014

### LuukS

Hi Dauto,

That is pretty clear. So you meant that the distance between the mirror and the slide projector should be the same as the focal distance?

It's going to be an artwork...

8. Apr 19, 2014

### Simon Bridge

Since it is an artwork - what do you want the audience to see?
I suspect you want the audience to see a beam of light from the projector anglinging into the lens or something like that?

Dauto is telling you that if the lens of the projector is at twice the focal length, the image of the projector lens will be at the lens position. If you defocus the projector so it sends almost parallel light, then the effect would be of two cones of light inside a cylinder of light - their apexes meeting at the focus.

Once you've set that up you can fine-tune for what you want.

Note: you'll only see the light beam in a dusty room. I don't know how strong the effect would be.
Putting a filter on the mirror (thin colored plastic) may make the returning beam a different color.

9. Apr 19, 2014

### Baluncore

Large sheets of retro-reflective material for printing road signs are available. By having many three corner reflectors in their surface these reflect the majority of incident light back the way it came.

If you use a flat area of such sheets instead of a spherical mirror, you may get the result you are looking for without the mirror alignment problems. Use a white reflective material so it does not filter the colour of your image.

10. Apr 20, 2014

### LuukS

Ok that is pretty clear then! I'll try to get a mirror with a focal point of 500mm, and I'll experiment with that.

I am not sure yet what I want my audience to see. I got interested in the etymology of the word 'projecting'. Projecting is a kind of 'throwing ahead'. I thought it would be interesting to try the opposite, which would be something like 'injecting'. That's the starting point, now I need to try it and then I'll see what is interesting about this.

I'll upload a picture once I get it working!

Thank you very much!

11. Apr 20, 2014

### LuukS

Thank you, it might be nice to try this as well! I'll see if I can get some around here.

12. Apr 20, 2014

### sophiecentaur

All that is necessary for the light to follow a reciprocal path back into the projector is that the curvature of the mirror is chosen so that light strikes each point on the mirror normally. If you could identify a centre from which all the light originates, that would have to be the centre of the mirror sphere. I think that a retroreflective sheet would not satisfy the phase requirements for the optics to work as seems to be required.

13. Apr 20, 2014

### LuukS

The centre would be the lens of the slide projector. The diameter of the mirror = twice the focal length. So if I place the mirror at twice the focal length from the projector the light source will be in the middle of the circle.
Thank you!

14. Apr 20, 2014

### Baluncore

The light source is not coherent, also it radiates along variant paths through the image being projected, so there is no requirement that the mirror be phase correct.

The disadvantage of a retroreflector is that it has more scattering than an accurate polished mirror, but for an art installation that might be an advantage.

15. Apr 20, 2014

### Simon Bridge

What sort of mirror is wanted depends on what the audience is expected to look at and how the projector lens works. These are usually set to produce a magnified image so the light from the projector diverges. To get that light back into the projector, you want the reflected rays to converge - which is probably behind the idea of using a concave mirror.

Putting the lens at about twice the focal length from a (spherical) concave mirror should do this.

Since what the audience is to look at has not actually been decided yet, it is probably too soon to discuss materials in any detail. There are lots of options. Need more data.

Last edited: Apr 20, 2014
16. Apr 22, 2014

### LuukS

17. Apr 22, 2014

### Simon Bridge

I'd experiment with cheap mirrors though.
You can get spherical shop-mirrors very cheap and they are reflective on both sides.

18. Apr 23, 2014

### sophiecentaur

This would be a novel thing for you to do for yourself but the audience could not be aware of anything happening. Did you consider angling the reflector so that a 24X36 image is formed on a small screen, right beside the projector? A small amount of smoke (or a healthy alternative) in the air would show the ray pattern quite effectively
That's the Physicist in me, talking and not the Conceptual Artist.

One thing you may need to consider would be the vast difference in brightness of the light levels inside the projector and the brightness of your final image. Your worry about overheating is unfounded, I think as there would be no more heat turning up inside the projector, with the reflected beam, than there would be with a totally black slide in the holder, absorbing all the light, first time through.