# The physics behind Google Glass' “prism”

In writing a bachelor's thesis about applicable use cases for Google Glass in retail I also strive to explain the physics behind Glass' optics. So far I've come to the following conclusions:

1. Glass must use a concave mirror (the reflection layer in this image) to magnify the image projected by it's LCoS Display and project it at infinite distance
2. In addition to the concave mirror, it must use some sort of either one-way-mirror or beam splitter (shown here as the diagonal piece) to reflect the concave mirror image to the user

So here's what I think happens (I'm not proficient in physics at all, so please don't mind the inaccurate rays ^^)

Assuming this is how everything works, here's what I don't get yet:

1. How does the concave mirror project the magnified virtual image into a distance of according to the Google FAQs around 2.5 meters or 8 feet in front of one's eye? Does it have something to do with the distance from the focal point of the mirror to the actual light source?
2. Assuming 3 is actually a one-way mirror (or semi-transparent), speaking in terms of ray orientation, a perceived distance of 2.5m should equal nearly parallel rays, right? In that case, the mirror should already be reflecting parallel rays, right? If that's the case, how does the concave mirror, which enlarges the image, produce parallel rays to place the image at infinity?
3. Looking through Glass on your head gives you the enlarged image at infinity. Looking through the other side gives a horizontally mirrored small version of the original image. Why is this? I thought if 3 a semi-transparent mirror, it should reflect the enlarged image of 2, thus one should also be able to see the enlarged image through the other side. Instead, this is what happens: I could explain the fact that you see the small original version of the image due to the fact that the mirror is semi-transparent and thus reflects 50% of the original image back out the other side. But if it is semi-transparent, why can't I see the enlarged image through the backside as well?

I'm sorry if these seem like basic questions to you, I'm trying really hard to understand all the inner workings of the device and have not had any real physics education since 8th grade now..

If you need any more pictures or a more detailed explanation of specific parts, I can deliver all of that :)

Already a profound thanks for helping me out!

• Did you try to find relevant patents? Hopefully including useful illustrations - I'm not thinking of decoding the text ;) – Volker Siegel Jul 2 '14 at 10:54
• Indeed, I did try, but all illustrations are even more basic than mine above. No way of telling how the whole thing works without trying to decrypt the text - which, at least for me, is nigh impossible. Edit The only description I found for the prism was this: "...and to make that image visible to a user by looking into a viewing side 60 of prism 54. This can be done by making prism 54 with a specific shape and or material characteristics.", which is not very specific. Interestingly they clearly display the diagonal mirror on the patent images, but it's never being referred to in the text. – Philipp Christoph Jul 2 '14 at 12:29
• (Technically, a patent text is not even only encrypted, it's worse: The plain text itself it made to be not understood! :) ) – Volker Siegel Jul 2 '14 at 12:43
• When I see the word 'one-way mirror' I tend to start shaking! :P – DoublyNegative Apr 10 at 19:40

So taking your questions one at a time 1) The concave mirror will form a virtual image if the object is placed closer to the mirror than the focal point of the mirror. The formula for the position of the final image is $s'=\frac{sf}{s-f}$ where s is the object-mirror distance and f is the focal length of the mirror. You can see that if $s<f$ this will be negative which implies a virtual image. The virtual image means the rays do not actually meet but appear to come from a point. In the diagram I have drawn real rays as solid and virtual rays dotted. So in the google glass case the LCoS screen must be closer to the mirror than the focal point (indeed from your photo of the prism you can see the curved edge is very slight implying quite a long focal length - on my diagram I rather exaggerated the curvature). The presence of the 45 degree mirror turns the real rays toward the eye while maintaining their relative angles and so the virtual rays now appear to come from a point straight ahead of the viewer.