When I look in the mirror are my eyes focussing on the surface of the mirror or at the reflection?
For example, if I stand 1 metre away from a mirror and look at the reflection of something one metres behind me, are my eyes focussed at 1 metre or 3 metres (1 metre from me to the mirror and 2 metres from the mirror to the object)?
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mirror me object
Three meters. My optician has a very small examining room, so he projects the chart into a mirror for the eye test.
The distance to the image in the mirror from the surface is the same as the distance from the actual object to the surface of the mirror. Try it with an SLR camera.
The object.
I have just tested this theory using a window, not a mirror, but here’s my methodology: In the window, I can see reflected a wall several yards behind me as I face the window. Through the window, I can see a plant a few inches on the other side of the window.
Shifting my focus from the plant to the reflection of the wall, I can feel my eyes shifting their focus entirely too much for the mere inches between the glass and the plant.
Conclusion, I am shifting my focus from the plant, at nearly the same distance from me as the glass, to a distance equal to the distance from me to the glass to the wall behind me.
WAG quotient of this answer: 8%
Note that if you were focusing on the mirror only, either every object in it should be blurry or you could perfectly see anything just by holding up a mirror to it, since a flat mirror cannot focus any light.
If it’s a curved mirrored surface, though, then you would have a different answer.
The actual object. When I’d do a shot on a film that involved a mirror look, the camera assistant would measure the distance to the mirror, THEN tape measure again the distance out to the actual object.
Add the two, that is the critical focus mark. That allows neato things like a long lens shot of the reflected object, then a slow rack focus to the mirror itself, etc.
Cartooniverse
Nope. You’re focusing on the mirror or the object. It depends.
The thing that’s clearest in most mirrors is the object being reflected. But the mirror isn’t completely transparent, and if it’s dirty or clouded (say shaving in the morning…) then your eyes might focus on the mirror.
Mirror, mirror on the wall … 
Simple experiment: Stand in front of a mirror. Hold an opject, such as a comb, up against your reflection in the mirror and then notice that you have to switch your focus when you look between the comb and your reflection.
OK, it kind of makes sense, I think. So where is my focus? In the example I gave in the OP, am I focussing at 3 metres (me to the mirror + mirror to object) or 2 metres (object to mirror)?
Does this mean that if I focussed on the mirror the object that is reflected would be out of focus?
The other question I have is why is it so? And how to my eyes figure out what to look at and how to focus?
Ick. How misleading. The important thing to remember is that your eyes have no “idea” that there is such a thing as reflection; as far as they “know,” you are seeing an object beyond the plane of the mirror. The light travelled three meters from the object to the mirror to your eye, so it “looks” three meters away.
Your eyes focus wherever your brain tells them to; when you look at an object, your brain tells your eyes to adjust the thickness of your lens until the light reflected from that object converges clearly on your retina. When you focus on the mirror itself, you get a clear image of toothpaste stains, but the light reflected from an object, off the mirror, and to your eyes has a different path than light that goes directly from the light source to the mirror.
Being someone who is nearsighted, I am unable to focus on a distant object in a mirror without my glasses, even if I stand right up close to the mirror.
As several folks have noted, you are looking at the reflection of the object in the mirror, so your focus is set to the distance of you from the mirror plus the distance of the object from the mirror. (Unless, that is, you’re actually focusing on the dust on the mirror or something).
People who tried to use the Polaroid SX-70 or other auto-focussing cameras found that their photos were out of focus when the had a window in the way, or if they “banked” the shot off a mirror. The camera’s ultrasonic sensor set the focus based on th distance to the mirror or window, you see.