Why can our eyes focus on certain things in a mirror if it’s a two-dimensional object?

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Didn’t know how to flair this, sorry.

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If you consider that a mirror is doing nothing but reflecting light (visual data), and the objects that are reflecting/emitting light into the mirror are positioned at different distances and orientations relative to the mirror. Accordingly, the signals we would perceive from the light off those objects (i.e. color, shape, depth) is still reaching our eye, but is just reflecting off the mirror first. The information in that light is largely unchanged, allowing us to still determine closer and farther objects, the color of objects, and focus on them individually.

Our eyes didn’t evolve to deal with mirrors and reflections. Your brain and eyes ALWAYS assume that there’s a way to interpret what your seeing as objects in 3D space with nothing between you and it.

When you look at a mirror, because of how reflections work, there’s always a “false” solution to the question of “where did this light originate from?” that appears to be an ordinary object behind the mirror. All the properties of light that we’d use to determine depth — blur, angle of divergence, shadows, environmental cues, parallax — are all preserved in a mirror, meaning that there’s no way for us to distinguish the two in a mirror with our eyes alone.

Interestingly, with the right combination of polarizing filters, you can actually distinguish the original from a reflection, but humans cannot innately detect the polarization of light with the naked eye, so that trick normally doesn’t work.

Because your eyes are not focussing on the mirror itself, but on the object. If an object is say 5 m away from a mirror and you’re 3 m away from that same mirror, you’d have to focus your eyes as if you were looking at an object 8 m away. The lines of sight of your eyes won’t cross on the mirror, but on the point you’re looking at whith the mirror simply redirecting the beams.

If a mirror would be pretty dirty you’d find that it would not be possible to focus on the dirt on the mirror (at this point you’re looking at the 2D mirror itself) and the objects in the mirror (the 3D room that the mirror is reflecting).

It’s hard to explain without drawing this, so sorry for the rather bad explanation.

You are still using binocular vision, and physics still applies. Your eyes (assuming you have 2) each sense the arriving light independently from one another, and your brain calculates the arrival paths to determine an estimate for distance.
The mirror functions to literally “fold” the path of light arriving to your eye. The distance the lights travels from the object to your eyes does not change. It’s really no different (conceptually) than looking through a window.