We know that a plane mirror can reflect rays more precisely so we can get a more accurate image. So why can't we use a plane mirror instead of a projection screen?
[Physics] Why don’t we use a plane mirror instead of projection screen
reflectionvisible-light
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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.
2) You're right that at 2.5m the rays from the virtual image will be nearly parallel but it's still not infinity. Parallel rays would only result if the LCoS screen was actually at the focal point. At 2.5 m the normal eye can comfortably focus on the image when needed while allowing it to blur out when focusing at more distant or closer objects in the real world.
3) To the mirror: It is hard to tell but this is probably just formed by having two slightly different refractive index materials. Ideally lower on the right than on the left. This means the reflection from concave mirror to the eye will be by total internal reflection and so will be quite bright. Where as the spurious first reflection (shown by narrow lines in the diagram) will be a dim partial reflection. It is the image from this reflection you see when looking from the wrong side. You don't see the other image because the rays from it are directed away to the eye. It is possible there is a further partial reflection from the eye-side flat surface but you are not likely to see this because its rays will be mostly reflected back toward the concave surface by TIR. It's very likely this surface is in any case anti-reflection coated to stop just such spurious images. If they had used a partially silvered mirror instead of a prism then you might see some light from the main image on the wrong side due to dust scattering on the mirror surface but it would be a very blurred image. Using a bonded prism pair, probably assembled in a clean-room, this shouldn't ever happen here.
It's a pretty clever little arrangement! There is a neat little java app here where your can play with the imaging properties of concave mirrors. It's a little old so I had to add it to my exception list as modern Java complained it was a security risk.
This is entirely based on the way light interacts with the materials. Mirrors are made of materials particularly chosen because they reflect light without distorting it.
Some materials might reflect a lot of light, but the light might (essentially) "bounce" around inside the material in such a way that it comes out at odd angles or with odd colorings in a way that distorts the image. I use quotes because light in the way it propagates through mediums is best described as a wave, and you have to be careful about how exactly you think of a wave "bouncing off" atoms and their electric fields and such. But anyways this distortion is similar to the way frosted glass distorts light passing through it in bathrooms, except that this would be a case of transmission of light, not reflection of light as with a mirror.
Some materials absorb the light, only to re-emit it later. These re-emission usually bear little resemblance to the light waves that originally hit such a material. Similarly, some materials are very selective about what colors and wavelengths of light they reflect and absorb.
All of these latter considerations provide a large class of materials which end up not making good mirrors.
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Best Answer
Using a plane mirror would be a problem only because it can reflect the rays more precisely or what can be called as a specular reflection.Using a screen rather than a mirror would make the reflection diffuse in almost all directions equally called as a diffused reflection.Using diffused reflection rather than specular reflection is important and this could be explained using a simple analogy.Consider the objects you see in daily life they can be seen from any direction because they diffusely reflect the light whereas the image you see on a mirror changes with the direction of your view.Using a mirror would make the image appear different for different audience.The left part of the diverging beam falling onto the mirror would mostly reflect to the left side and can only be seen by the audience on the left side and vice-versa.This wouldn't be a case with a screen which diffuses light falling onto it.