How far will the imaging be? And is it possible to make it farther?

So currently I'm trying to make a smart glasses, where you have a projector that projects an image onto transparent flat glass, and some of the light will reflect into your eyes (something like the image below, viewing from top).

-----------------------------(glasses)
(projector)
(eye)


So my first question will be, how can I calculate where the virtual image will be image at? (By knowing the dimension of projecting source, the distance from projector to glass, and the distance from the glass to the eye.)

And next, by not changing the distance between three objects, is it possible to make the virtual image image farther from the eye? (As the farther the image image, the image will be bigger.)

• If the glass is flat, then you could imagine the projector being on the other side. That makes it easier to trace the rays and think about this problem. And when you do that you will see that the image you can see will span an angle that is no bigger than the lens of the projector. This should give you something to think about... and basically tell you that you probably want non-flat glass... – Floris May 17 at 14:23
• @Floris But if I use non-flat glass that means if I look through the glasses it'll twist my views (and I don't have an issue like near sight). Otherwise, is it possible to make the projection look bigger by adding convex lens in front of the projector? – Andrew.Wolphoe May 17 at 14:25
• If both surfaces of the lens are parallel (curvature centered on the same point) you can get magnification of the projection without really distorting the image of the world beyond. See this article for a nice description of current approaches to AR: medium.com/@RDelly/… – Floris May 17 at 14:43
• @Floris replying to your first comment. After thinking for a while, still can't figure why you won't see projection no bigger then the lens of the projector? Isn't the projection be bigger as it's farther from the projector? As the light path of the projection should be like a cone. – Andrew.Wolphoe May 17 at 23:35
• no rays can reach your eyes that didn’t pass through the lens of the projector. So if the lens of the projector is small the field of view (range of angles from which light reaches your eyes) will also be small. Hence the value of a curved mirror (which magnified the size of the projector lens). – Floris May 17 at 23:39