Physics Mirrors

So let's talk about mirrors and image formation now before I get too much into this I really want to talk about what it means to be an image. Alright so what happens is we take an object and we put it in front of a mirror the light reflects off of that object then goes and reflects off of the mirror and then the important thing is what happens to the light after it reflects off the mirror. Alright the idea is that sometimes this light will reflect off the mirror and then come back together again so that means that it's going to reform that same image. It's going to look just like it did when it reflected off of the object and so that's what we mean by an image it looks like an object. Now if light actually goes through the image so that it reflects off and it comes back through and reconvenes then we call that image real. Okay that image is real, if on the other hand it just looks like there's an image and in fact the light never reconvened at all then that image will be called virtual okay.

We'll find that if you use only a single mirror or a single lens then real images are always inverted that means they're always up-side-down so you're looking through the lens the object is right side up, the image is up-side-down alright. Virtual images on the other hand will always be erect or right side up okay if there's a single mirror or a single lens. And then of course we can have magnification, magnification is always given by the ratio of how far the image is from the mirror divided by how far the object is from the mirror. Alright so let's just do this real quickly with the simplest case, that of a plane mirror. Alright a plane mirror goes like this, we've got light coming from the object and it just reflects straight back, so there's one of them. Let's draw another one, well I've got light from the object and then it just reflects and remember angle of reflection equals angle of incidence so it's going to go like that.

Now here's the question, are these 2 rays ever going to recombine? Well it certainly doesn't look like it right they're just getting further and further apart. So what would I mean by an image? I mean I stand in front of a plane mirror I see an image, here's the idea, when I stand in front of a plane mirror I see these two light rays but my brain doesn't automatically think about the mirror being there it just says okay there's those two lights rays. So it extrapolates the light rays back as if the mirror wasn't there and so look and it looks like. It looks like the light came from here look at that, same distance behind the mirror as the object was in front of the mirror, same size as the object that's the image. Notice that the image is erect it's right side up and it's the same size and same distance away. So we have a virtual image because the light never actually was here if I go and look behind the mirror I'm not going to see anything there right? Well I'll see a wall okay. So the idea is no light actually came here so virtual erect image, same distance away from the mirror as the object with a magnification of 1 alright which means it's not magnified.

Alright so let's look at a slightly more complicated cases and these are the cases associated with curved mirrors. But we need to do this kind of carefully, there's 3 major cases the concave mirror 2 cases of that and the convex mirror only 1 case there so that will be nice. Alright let's look at the concave mirror first, alright if the object is far away from the mirror, how far depends on how concave it is, how curved in it is. But if the object is far, let's draw a couple of these rays, let's draw 1 to the vertex alright it's going to reflect off same angle it came in at. Alright and then we'll do 1 straight out so we'll do 1 just like this and it reflects at the same angle it came in at, but remember that angle is measured off of the normal. So I got to draw me a little normal alright and then I got to draw the reflector and look at that, we do have these rays recombining. So this gives us a real image but notice that the real image is inverted okay so this is going to give me real inverted image alright it's going to be closer the magnification will be less than 1 alright and so this is what happens. Now let's think about what will happen if I start moving this object.

It turns out what happens is as the object moves closer and closer and closer to the mirror the image moves further and further and further away. Alright these 2 things will coincide at a distance that's equal to the radius of the circle that this would make if you made a circle it's called the radius of curvature how curvy is it, alright the more flat it is the bigger that radius is. The more curvy it is, the smaller that radius is, so these 2 things will come they'll overlap and then they'll go like this. The image will go off to infinity as the object goes to a certain place in front of the mirror called the focal length. Alright and that will be discussed in more detail in the segment on the lens equation. Alright so what happens if I get closer than the focal length? Well let's see again we'll draw 2 rays, there's one and then let's draw another, draw this one in green. So we'll go straight over and then remember I got to give myself my normal alright and these 2 are actually not, sorry these 2 are actually not going to overlap they're not going to ever recombine alright so I have to continue them backwards to see where my image is.

And my image is now over here much taller and virtual and erect so this one is virtual, erect. So basically the idea is with a concave mirror the object moves in closer to the mirror I have a real inverted image that moves out away from the mirror the 2 things coincide briefly and are the same size but one of them is real, well the object is obviously real. The image will be real and inverted and then the image goes out keeps on going out to infinity once the object reaches this certain point we go over here. And the image appears on the other side, it's now virtual and erect and as the object gets closer to the mirror, the image will also get closer to the mirror. Alright so that's concave, that's the most complicated case. Alright now let's do a easier case, let's do convex alright convex goes like this in like that and then again I need my little normal out like that. Alright so there's one let's do another one, here we go down like that. Notice that these 2 are obviously never going to recombine alright so that means that we've got a virtual image, we can determine where that is by continuing these Geometric lines and look what we end up with.

We end up with the rest of what was going on here, so the issue is that here we always have an erect virtual image that's further away from the mirror than the object. In the case we always have an erect virtual image that's closer to the mirror than the object. These mirrors are very, very useful in stores for example because everything has a small magnification at 1 and that means that if you use one of these convex mirrors you can see more, you can see more going on, you can see the whole store at once right, which is not the case with these concave mirrors. Concave mirrors are actually used to magnify things alright so those are some qualitative ideas about the way that mirrors and image formation works.