Projecting an image back into a slide projector

Hello,

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

Attachment 68797

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!

Attached Images

Spiegel Schets.jpg (44.4 KB)