Okay in today's video we're going to go
through drawing ray diagrams for concave mirrors and we want to be able to use those
ray diagrams to locate the image. Now here's the general diagram we're going to use we wanna kinda make sure we know the important parts of this diagram. The first one is
this white line, horizontal line that runs throught the center of the mirror we call that the principal axis. We
have the point C, centre of curvature we have the point f, the focal point, and the
focal point is at a distance we call the focal length from the mirror. C is the center of curvature this is a spherical mirror it's a big circle. You can think of a circular or spherical mirror, it's a big circle and C is at the center that circle so
really the distance from the Center of curvature, from C to the mirror is kind of radius of that circle you can think of it that way. We have this point f. Point f is at a
focal length away from the mirror and then you'll notice that f is betweenC
and the mirror so the focal length is 1/2 C okay? Now you remember for the convex lense video we had f and 2f and 2f was twice as far away as f but
now we have f and C. C is twice as far away as f
so really C and 2f are analagous positions, places on the principal axis it's just that for a mirror we call it C which is the center of curvature okay
now what we want to be able to do at the end this video is regardless of where we place the
object whether we have it beyond C, at C, between C and f, at f, or inside of f we are gonna be able to draw the ray
diagram and describe the image. And really, before you
even draw the ray diagram, after a little practice, you should be
able to describe the image before you even draw the ray diagram and
then you can just draw the ray diagram to let your teacher know you know how to draw the ray diagram and to confirm what you know about the
image and you should be able to say something about the location of the image on the
principal axis, the size of the image relative to the object, the orientation
on the image, and the type that the image. So here's our first problem this is
the general diagram we're going to use again here is the object, here's the principal
axis, here's the mirror, and you, your eye and the object are on the same side as the mirror if you think about how you use a mirror usually looking at something oftentimes it's
your face okay? so here's the object and we need to draw
the ray diagram and before we do that I just wanna remind
you of whether it's a concave mirror, convex lens, a concave lense, or a convex mirror you should notice that
for all four of those things the ray diagrams are basically drawn the same way so you don't have to memorize a bunch of
different ways to draw the ray diagrams. You just have to memorize the two or
three rules that we're going to use and then you can apply those rules to
all four of those optical devices okay? So for example, for
the concave mirror the first ray we draw, we're gonna draw
from the tip of the object and it always goes into the mirror parallel to the principal axis. So this light ray comes off the object, it goes into the
mirror parallel to the principal axis and it comes
out through f. So it goes like that so this one has has to be parallel and this ray, when it's reflected off of the mirror must go through f. It's just not some
random angle, this angle in here, it's drawn so that it goes through f and you should
have a nice straight edge and a nice sharp pen or pencil preferably
incase you make a mistake and you draw your ray diagrams okay? Always use a straight edge it's not a
freehand sketch. Alright the next one goes into the mirror through f and then comes out parallel.
So this one's the opposite the first one we drew was parallel, f. This one is f, parallel and on those the lines
intersect, the rays intersect right there and that is where the image appears okay? Now based on that ray diagram we can
say about the image that when the object is beyond C, greater than C away from the
mirror the image will always be somewhere between C and 2f. The image will always be smaller
than the object. When the object is greater than C away the image will always be inverted and will
always be a real image. It's an image that is created by
converging light rays and they converge right there
at that point okay? So before you go on let's just review this
we drew two rays parallel was the first one, f. I like to call the first one parallel-f because it goes in parallel and comes out
through f. Then the next one, the second one goes in through f and then comes out parallel so they're opposites of each other. Now we're going to do the exact same thing now we have moved the object so that is right at C. So we're gonna go
parallel, f f, parallel and you'll notice that the image appears right there it's at the same place as the object right at C so when they
object is at C the image must also be at C or will
always be at C. it'll always be the same size. It'll always be inverted and it's still
a real image created by converging light rays. Okay so those two were basically drawn
the same way. The third one we're going to do the same
thing again; now we haved moved the object so it's between C and f. So I pick up my nice sharp
pencil and my straight edge and I draw my first ray going in parallel, coming up through f. It must go through
this point. The next one goes in through f, comes out
parallel. So once again it must go through
this point you have to draw through this point it's not just some
random angle or so random ray it's the one that goes through f and there is the image and you'll notice
now that the object is between C and f the image will
always be greater than C away from the mirror. The image distance is greater than C thats what d-i stands for: image distance. The image will always be
magnified, it's bigger than the object. The image
will always be inverted and it's still a real image okay? So you should notice for the first three
we drew them all exactly the same way: parallel-f, f-parallel and the image appears where
those light rays converge, those light rays cross. Okay now this one's a little different; we're going to a first ray exactly the
same parallel-f. Now we can't really draw the f-parallel because we're right at f. We have moved the object so it's right at the focal point. So what we're going to do is draw a
second ray that comes in and strikes the mirror right at
the principal axis like that and then it's going to reflect at an
equal angle. So this angle the angle of incidence and the angle of reflection have to be the same and you'll notice
when we're right at f these light rays do not converge they're
parallel. In order to get an image as in the
previous three examples the light rays must converge they must
cross parallel rays don't cross. Therefore when you're at the focal point,
when the object is at the focal point, when d-0 equals f there is no image ever at all because those light rays are parallel
light rays. Okay so we drew that one a little differently
but it's the same general idea. Okay here is the last one now finally
we're inside of f, the object is inside the focal point and you're going to do same thing with
the first one parallel-f. Now the second one we're gonna draw the same way we're going to go too the principal axis and its gonna reflect at the same angle so
that the angle of incidence, this angle and the angle of reflection, this angle
are exactly the same and you'll notice these light rays don't
converge. They're not parallel but they actually
diverge. Now your eye is over here; it sees these light rays coming towards it. It notices that the light rays are
traveling in a straight line and it doesn't know about any of these reflections off of the mirror so
as soon as they travel in a straight line and your brain, your eye follows those
light rays back. It's looking for the intersection of those light rays and if you follow them
back you draw them nicely with your straight edge and your ruler... You'll notice that those light rays
converge right there behind the mirror okay so when you're inside the focal point you'll notice now our image is behind the mirror, so it's
located behind the mirror and you'll notice that it's
switched from being upside down, inverted to being right side up which we
technically call erect. You'll notice it's magnified, its
bigger and you'll notice that well this is a
virtual image. The virtual image is an image that is created by diverging light rays that your eye follows
back behind the mirror. If you have a makeup mirror which a lot
of women do for putting on their makeup you'll notice it's
curved mirror and you have to get really close to the mirror and then your eye appears really big and if you concentrate a
little bit you'll notice that your eye looks like it's
coming from behind the mirror okay but it's not. It just
appears to come from behind there that is a virtual image okay. So there we
go those are the five cases you should be able
to draw them all now carefully straight edge, sharp pencil, make sure all
your lines are straight parallel and all that stuff. Now this is a somewhat complicated looking table that summarizes
the results of the information we gathered from
the video. This is for the concave mirror, this is the object distance we had
greater than C, at C between C and f, at f, and less than f away. This is the
information for the image. The image distance, the image orientation,
the size, and the type now on here I have the table for the concave mirrors and the table for the [convex] lenses.
These are both converging devices light rays converge when they come into
these devices and you should notice that the
answers, the stuff in this gold color, the answers are exactly the same for the
convex lens and the concave mirror. For example when
the object is at C the image is at C, it's inverted, it's the
same size, and it's real. For the convex lens when the object is at 2f remember 2f and C are the same place on the principal axis: twice the focal length. When the object
is at 2f for the convex lens the image is at 2f, it's inverted, it's equal in size, and it's real. Let's look at one more
case When you're inside of f, the image appears behind the mirror when you're inside of f, the image appears behind the lens. When
you're inside of f, the orientation is erect or upright. When you're inside of f the orientation is erect. When you're inside of f, the image
is magnified and it's a virtual image same thing here
magnified and virtual the point being you don't have to
memorize the answers for ten different cases. All you have to do is realize the
pattern as the object gets closer to the lens or the mirror, the image gets further away and bigger
and it switches from being upside down to right side up
when you're inside the focal point. Okay so don't memorize them learn the
rules, learn the pattern it will be much easier the answers for the
concave mirror and the convex lens are exactly the
same. Okay so I know that's a lot of information but draw your ray diagrams, think about it a little bit, and it will all come together very
nicely. Thank you very much for watching, I hope that was helpful and we'll see you in
the next lens and mirror video!