- Geometrical optics is a branch of physics that inquires about the way light travels in the form of rays.
- Contrary to the popular belief, mirrors do not reverse things left to right, they reflect backward.
- Mirrors change the appearance of what is in front of them along the direction of the Z-Axis.
We use them when we groom, we use them for decoration, we use them for many other optical and scientific pieces of equipment like telescopes and cameras. Mirrors are interesting objects indeed, reflecting what is in front of them, as well as the ways of our culture.
But, how much do we know about how they work and the science behind them? Why does it seem that mirrors invert left and right, and not up and down? To answer these and similar questions, the best way is to experiment with examples!
How Do Mirrors Work?
It is time to explore a little bit of basic geometry, or to be more precise - geometrical optics. Looking into a mirror, you might be inclined to think that mirrors reverse things left to right. However, they do not do that, they do not reverse anything per se, it is we who do the reversing. The particles of light reflect off the glass and the image that appears in front of the mirror is reflected backward. Do not be fooled, it is a simple inversion of front and back, there is no side-switching.
You can test this with a Robert DeNiro impersonation from the Martin Scorsese's Taxi Driver. Stand in front of a mirror and point your finger gun (we will use a hand gesture instead of a real gun for your safety) straight in the mirror. The barrel of the gun (or in this case, your forefinger) will be pointing towards you (the opposite direction) because the light will travel in the same direction from which it came.
Now, imagine that Robert DeNiro is standing on your right side and both of you are pointing towards the mirror holding your finger guns. What will happen? Well, your forefingers will point in the opposite direction like in the previous example, but it will also appear that DeNiro is on your left side, instead of your right side. Why does this happen? How does a mirror differentiate between the x and y in terms of direction?
Mirror, Mirror On The Wall, Who's The Fairest Of Them All?
The reason this happens is that the mirrors are flipping objects along the z-direction. Basically, in the Cartesian coordinate system, the X-axis is left and right, Y-axis is up and down, and Z-axis is forwards and backward. Since we are accustomed to observing objects along the X-axis and Y-axis, it can be hard for us to visualize the forwards and backward direction of the Z-axis.
This confusion might arise due to our familiarity with photography because when we look at a photograph in our hands, we rotate the photograph so that it faces us. For example, you took a selfie with a polaroid camera and you are holding the picture in your hands, looking at its unparalleled beauty.
However, once you did that you rotated the picture around its Y-axis. If you proceed to look at your right ear in the photograph, you are in fact looking at your left ear. If you look at yourself in the mirror these directions will not be changed like they are in the photograph, but if you turn it so that it is facing the same direction as you are, your left ear will be at your left again. It is not the mirrors who do the flipping, it is us.