# Figuring out Lens Magnification to be Able to Focus on Screen in Front of Face

Being very interested in how VR/AR headsets work, I want to figure out the physics of looking at a screen right in front of one's face, figuring out the limits and parameters to what one could potentially focus on.

In particular, let's suppose we have a simple system defined by d1, d2, and m where:

• d1 is the distance from eye to lens,
• d2 is the distance from eye to object (phone), and
• m is the lens magnification; for example a typical fresnel lens sheet out of plastic, which are cheap and thin.

The question is, given the constraint of the human being able to comfortably see the screen without straining eyes (related to human focal length I'm assuming?), what is the shortest d2 we can make, and how does it depend on d1 and m? We can assume some standard screen size such as 7cm x 21cm.

I'm not sure how to approach the problem partly because I don't know how to define what a human can comfortably focus on. I've read online that approximate human eye focal length is anywhere from 17mm to 22mm, which may be a useful starting point.

• Thanks for your answer, it's a little abstract but I think it's making some sense. Do you know in a more concrete way how d1, d2, and m may interact? Given the human eye focal length?
• @JDS what really matters is p and q in the Lensmaker's Formula $\frac{1}{f} = \frac{1}{p} + \frac{1}{q}$ for the lens m . you want to choose p,q,and f so that the diverging cone between m and the eye's lens is no larger than the lens (so no loss of light), and that the virtual image at distnance q from the lens m is a comfortable focus distance frm the eye's lens (thus d1 + q) May 6 at 11:24