So what have we learned so far. Well, what we see in the mirror depends both on what rotation axis is used to see the image and on how our brain works but this isn’t the whole story for as we have seen we can convert one type of rotation into another but it really doesn’t explain the image reversals in either case. To do that we have to understand the interesting concept of inversion. Inversion is probably the most difficult concept we will discuss but it is important to understanding not only mirror reflections but a lot of modern physics.

Let’s start by doing another experiment. This time just stand in front of a mirror and raise your right hand. The situation is illustrated in the image at right. Notice that the image of the hand raised in the mirror is still on your right side but it appears to be the left hand of the mirror image. This an example of inversion and we’ll discuss the reasons why this happens later. Here the inversion is like you sort of melted in the mirror turning yourself inside out so that your back becomes your front while your front becomes your back. That is, your mirror image is facing you. If it were an exact copy it would be facing away from you. In order to see the image facing you the back of an exact copy has to be moved to the front without any rotation. This exchange of position without a rotation is what called an inversion.

It’s perhaps easier to see this using a thin piece of paper you’ve written your name on in very dark letters. Hold it up in the light so that you can see the letters from behind (doing a vertical rotation). The letters you see appear backwards just like in a mirror. Its as if we magically moved the back to the front. This is what happens in a mirror. The image you see in a mirror is a combination of a rotation and an inversion. Notice that the image looks exactly the same except for the inversion and this sameness is what is meant by inversion symmetry and is an important concept in physics. Had you done a horizontal rotation you would have seen the letters upside down just like in a mirror. Try it and see for yourself.

Okay, so why does inversion happen in a mirror image? Well, to answer that we have to learn something about light. Light is a very special thing. In physics we have learned that everything in nature has a dual personality. That is, everything sometimes acts like a particle like a baseball or tennis ball and at other times it behaves like a wave like the waves you can create in a bathtub by wiggling your hand (gently, I don’t want your mother yelling at me!). This dual nature of things is very apparent with light. Ordinarily things behave mostly as either a particle or a wave but light exhibits both in the extreme.

In addition light has some very special properties. It travels very fast and unlike other particles its speed does not depend on fast the light source is traveling nor does it depend on how fast the the medium in which the wave is traveling through is going (for water waves the medium would the water). In fact, in a vacuum, the speed of light is a constant; one of the fundamental constants of the Universe. This was proved by a very famous physics experiment called the Michelson–Morley experiment . Light is an example of what is called electro-magnetic radiation. Other examples are radio waves, gamma rays, infrared waves and so on. They are all basically the same thing except for a particular property called frequency which I’ll discuss another time if you would like to learn more about light.

Light is also special because it has no mass (that is, the light particles called photons, unlike all other particles, don’t weigh anything). As a result the trajectory or path that the light particles travel is only minutely affected by gravity. In fact, when traveling through space, light generally behaves like a wave that travels more or less in a straight line at a constant speed as long as there are no obstacles in its path. This not strictly true but is a close enough approximation for figuring out how a mirror works.

In order figure out what’s happening when light reflects off a mirror we have to be able to describe the path that the light particles travel. A light path shows us where the light has been not where it is. For example, take a pencil and draw a line on a piece of paper. The line is the path where the pencil has been but not where the pencil is now. However, unlike the pencil line, we have to imagine what a light path looks like (it takes a lot of imagining to figure out the Universe). When a lot of light photons (light particles) follow each other, one after another, then we get a beam of light. Sometimes when you shine a flashlight or laser in the dark you can seem the light beam. Notice that the beam follows a straight line path.

The path that light photons travel has a special name. It is call a ray or light ray and the branch of physics that studies light under this approximation is called ray optics.

Okay so far? Now would be a good time to pause and think about what we’ve covered before continuing.

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Tags: Physics, Science

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