Image Formation by Spherical Mirrors (Ray Diagrams) Video Lecture - Physics

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.