If a mirror inverts left-right (lateral inversion) then why not top-bottom as well?

The short answer to this age-old question is that it does.  To see how it does you unfortunately need to read what comes below.  However – what I find much more interesting is why we have difficulty in understanding what is going on with mirrors – perhaps the simplest “optical device” known to man.  Why aren’t our brains “wired up” in such a way as to see the answer to these mirror questions immediately?

If you delve back into my posts on here you will find a pretty comprehensive explanation of how mirrors “laterally invert”.  There you will also find the answer to this “mirror question” – they don’t.  As I haven’t actually looked back to see what I wrote back then, I can’t remember if I covered the top-bottom inversion in a mirror, so I will do so here.

Everyone is aware of lateral inversion in a mirror, it occurs when we look into a mirror THAT IS IN THE VERTICAL PLANE, which is the “normal” place for a mirror as it is usually on a wall or somewhere similar so that we can shave or adjust our hair.  As I mentioned before – a mirror does no inverting at all – it merely reflects light straight back, that’s all.  If you are reading the words on a page in a book, and THEN ROTATE THE BOOK 180 DEGREES to see the words reflected in a mirror – then  of course it appears as if the words are laterally inverted.  The mirror simply reflects back to your eye what is placed directly in front of it, and what you have placed directly in front of it is a book that you rotated through 180 degrees giving the appearance of a lateral inversion of the letters on the page.  Simple, and a nice example of symmetry.  BUT – there is the relevant question, why not top-bottom reversal, and what is the symmetry requirement to see top-bottom reversal??

There is no top-bottom reversal in a vertically aligned mirror because you only rotated the book around in the horizontal plane, you didn’t also stand on your head.  O.K. but if that’s the case then by symmetry surely there is a way a mirror can invert top-bottom?  Yes there is.  Before giving the answer away, can you work out what you have to do to the mirror to see this?

The answer is that you need to move the mirror from the vertical plane to the horizontal plane – take it off the wall and lie it flat on the ground.  Now look at objects reflected in the mirror.  What do you see?  You have been aware of this effect all your conscious life.  You have stared at the surface of a still lake/pond and seen the reflection of distant objects from the water’s surface.  So why wasn’t it immediately obvious to you that the distant mountain’s reflection in the water was top-bottom inverted?  Because it is so obvious?  Then if it is so obvious why didn’t you automatically know the answer to the question – how does a mirror invert top-bottom then??

I’m really not sure why there is such confusion over this, but I’m pretty sure it has more to do with psychology and recognition that it does with Physics.

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