Hi. It’s Mr. Andersen and this AP Physics essentials video 121. It is on ray diagrams
drawn from mirrors. This is a beautiful picture of Jupiter and it is only there because we
have made telescopes made of mirrors that can take all the light, so this is a concave
mirror here, focusing it off of a plane mirror and then eventually to the observer. And the
bigger that mirror is the more of an image that we can have, or more detail. And the
Europeans are starting construction on what is called the extraordinarily large telescope.
To give you a sense of how large, here is a human for scale. And so it has a massive
mirror and so we can gather more of that light. And we have a better image. And so when light
hits a mirror it is reflected off the surface and it can create an image. The three mirrors
that we will look at are plane mirrors, concave mirrors and convex mirrors. But to figure
out where the image actually is you can draw in a series of rays which are straight lines
that represent where the light is moving. So if we draw in a plane mirror, for example,
and have rays moving towards it, from the right to the left, as they hit the surface
they are going to bounce right back. And so since we know that we can angle those rays
coming in at different angles and we can figure out where the image actually is. Concave mirror,
the way I remember it is it is like going into a cave. And so this part is going to
be the side of the mirror that is facing us, the observer. And so if we have that, as light
comes in we are going to get light bounced like this. So we will have a different image
versus a convex mirror. That is where it bends outward. We are going to have a totally different
image because it is kind of diverging away from that set parallel point. And so using
ray diagrams we can figure out where all of those rays go and therefore we can figure
out where is that image. Is it a real image or a virtual image. We will talk about that
in a second. And how big is that image actually going to be. And so let’s remember reflection
is going to be light bouncing off a surface. And our only rule is that the angle of incidence,
the angle between normal and the way at which the ray comes in is equal to the angle of
reflection. And so I took this picture of myself using a bozemanscience shirt. And I
took it with my phone using both the front facing and rear facing camera. And in the
rear facing camera I stood up to a mirror. So can you figure out which of these images
was taken using a mirror and which was not? Well, probably. And so let’s get to why
they look a little bit different. And so to draw a ray diagram for a plane mirror is fairly
simple. So let’s say this is our eye. This is the object. It is just an arrow pointed
up. And we want to draw how that mirror creates that image. Well the first thing you have
to realize is that there is going to be a virtual side to the mirror. And so every time
in a ray diagram you see dotted lines, that means that they are not real. They are virtual.
In other words you are facing a mirror and there is no area back here. It is just created
in your mind. You could not go visit it. It is a virtual area. And so the first thing
you do with a plane mirror is you draw the object in in an equal distance away from the
plane mirror. So I have drawn a virtual image. It is the same exact size. It is upright in
nature. Now we are just going to draw it in the ray diagram. And so what you do is you
choose a point on the top of the object and you draw a line straight to the eye. Now it
is dotted on this side because this is virtual remember and it is going to be a straight
line to my eye. We know the light is going into my eye. We do not shoot light out of
my eye. That is why the arrow is in this direction. Once I have done that, now I take that same
real object and I am going to draw a line like that. You can see the angle of incidence
equals the angle of reflection and it goes right back to my eye like that. Now we choose
a part of the object, let’s choose the bottom of the object and we do the same thing. To
my eye, virtual to real. And now I am going to draw that in the real world like that.
And now I have my ray diagram for my plane mirror. It is as simple as that. Again, draw
the virtual image on the other side and then connect the dots. And then make sure that
you have angle incidence equals the angle of reflection. And so why does it look weird
in a mirror? And what I mean weird is you noticed that my shirt was backwards. And so
with one of those selfies it looked like that. And on the other one it was reversed. So why
is that? Well what we are doing, I could turn it around and it would look normal, is that
the up-down, right-left is not being reflected. What is really being reflected is the plane
into the mirror. And so we get reflection of that. And so as your shirt, as you are
wearing the shirt, you are really wearing it not facing you but away from you. And that
away from you image is going to be what is reflected. And so let’s practice this. Imagine
you are standing next to a mirror and I ask you the following question. How large a mirror
do I need to see my whole image using a plane mirror? And so to practice I would encourage
you to pause the video and draw this one out. But I am going to do it for you right now.
And so the first thing you do is you create the virtual version of yourself on that side.
You then start at the top. And so I am going to draw an arrow to my eyes. How did it get
there? It went from the surface of my head, bounced off and came back to my eye. Now I
go to the bottom of the image. It goes to my eye and then I bounce it off like that.
And so if you make sure that it is going in the right direction, how big is the mirror
going to be? It is really small. It is actually going to be half of my height. And I can still
see my feet in the mirror because it is going to be reflected like that. Now let’s move
on to a concave mirror. So concave remember we are going into a cave like this and the
object is over here. And then the observer is somewhere out here. So you are looking
at the image. And so for this one we have to define a couple of points. First we have
the center of curvature, or the center of that mirror. So imagine that as a center,
so the radius to the mirror goes right back to that center point. We are also going to
add a focal point. So the focal point will become important in just a second. But when
you are drawing a ray diagram for a concave mirror what you will do is always start with
a ray that is parallel to the mirror. Then go through the focal point. Then you go through
the focal point and then go back to parallel. So let me show you what that looks like. So
you need to know where the focal point is. Also it is going to be half of the center
of curvature. Or you will see sometimes this written as f and this as 2f out here. But
again we are on this side of the image over here. First thing you do is you draw a ray
now from the real object, and it is going to be parallel to the mirror. And then that
ray is going to go through the focal point. And so that is what is neat about the focal
length and the focal point, is that if it is ever parallel to the mirror it is going
to bounce off. You can see the angle of incidence equals angle of reflection and it goes right
through the focal point like that. So first go parallel through focal. And now we are
going to take that same top of the image and we are going to turn it around. So now we
are going to draw through the focal and then that is going to create a parallel. So it
is the opposite of that rule. So now we look at where is the light coming? So here it is
coming out. Here it is coming out. And so where is our image going to be? Well it is
going to be right here. Now it is not a dotted line, it is a real true image right there.
So it is a real image. You can see that it is smaller in size and it is going to be inverted.
So it is going to be upside down. Now a real image you can take a piece of paper, put it
there and you would actually see the image on the paper itself. It is not a virtual image
at all. If you look at this, here is a concave mirror. So the camera man is taking a picture
of it and you can see the buildings behind him are inverted, upside down and they are
much smaller in size. And that is going to be a concave mirror. Now I move the object
up here to the center of curvature. I would encourage you again, pause the video and try
to draw this one out. But let me show you what it would look like. So you start at the
top. I am going to draw a parallel line, then where does it go? Through the focal point.
Now I am going to start at the top again through the focal and then it is going to go parallel.
And so where is my image going to be? It is going to be upside down like that. Now you
might be thinking how do I know where the bottom of it is? So image doing the same rules
on the bottom. So on the bottom we could go parallel back through focal. And then through
focal back to parallel. So the bottom is going to be right were the top of that image actually
was. So you can see now it is the same size. It is inverted. Let’s see what happens when
you move inside the focal length. You can see that we have zoomed in here. That is where
it gets a little bit crazy. And so this is the only different one you really have to
draw. So let me draw it again. So I am always going to start at the top of the object. I
go parallel to the mirror through the focal. So that seems easy. But now it is hard for
me to go through the focal. And so what I have to do is actually turn it around and
I would go through the focal like that. And now I draw it coming off parallel. So it is
a little bit different. But what is interesting you will note is that this ray and this ray
as they move away from the mirror, they are moving away from each other. They are not
converging at any point. They are diverging. And so that tells me I am going to find an
image on this side of the mirror. And so what I can do is I can take those two rays and
I can extend them into the virtual side of the mirror. And so where is the image going
to be? It is actually going to be on that virtual side. It is going to be larger is
size and it is going to be upright in nature. It seems a little bit crazy, and remember
once we get into the focal length then it gets a little bit crazy. So let’s make sure
this is true. So I have a simbucket simulation here. What you can do is you can move the
object on the left side. You can see that as I move the object on the left side we have
a real image that is inverted. I made it a little bit smaller so this works. Now we are
at the center of curvature. It is 2f, so it is upside down. But watch what happens as
we approach the focal length. That image is getting bigger and bigger and bigger and bigger.
Once we get to the focal length it really is not defined, that image. And then as we
move to the right side what are we going to see? The image jumps to the right side. It
is now a virtual image. It is going to be really really big. And it is going to be upright
in nature. And finally let’s go to the convex mirror now. So the convex mirror, we are on
this side of the mirror. And so same rules. What I do is draw a parallel. And now for
focus I am going to use the focus on the inside of the mirror. So it goes parallel and then
we get a bounce that is going to be through the focal point like that. Always be checking.
Is my angle of incidence equal to my angle of reflection? That looks all good. Next we
go focal to parallel. So it is going to go like that. Extend it through and now we are
going to parallel. And so if we do it like that you can see that there is divergence
over here but we can see the convergence back here. So where is that image going to be?
On this side it is going to be upright and it is going to be virtual in nature. It is
going to be smaller, reduced in size. Now if you have ever been on a bus and seen one
of those convex mirrors on the back, what do you see? Well the people in the back of
the bus are going to be upright. But they are also going to be diminished or smaller
in size. And so did you learn how to use data collection. Again I used a simbucket simulation
to make sure my ray diagrams matched up with what really happens. You could actually use
mirrors to do this and measure the distances. And then finally can you draw ray diagrams
for a plane mirror, a concave mirror, remember with concave you have to be both inside and
outside of the focal point, and a convex mirror? I hope so. And I hope that was helpful.