Concave and Convex Mirror Ray Diagrams - Ray, Optics & Optical Instruments Video Lecture - Class 12

okay everybody we are looking at curved
mirrors for the chapter 17 review all
I'm going to do on this is I'm going to
draw our five cases of the concave ray
diagrams and then I'm going to draw the
sixth case which is a convex ray diagram
all right
remember how I number these what I'm
going to do is I'm going to start from
the left this will be case one for an
object that is located there case two
will be located on C the center of
curvature case three will be in between
C and F four will be on f5 will be
inside of F so there's just going to be
a progression and we're just going to
work through cases one through five and
we're going to work our way closer and
closer to the mirror I'll remind you
since I kind of glossed over that that
these mirrors we could treat as a large
circle here okay so we are just grabbing
a portion of a circle and there's a
mirror on it so C is the center of
curvature it is associated with the
distance the radius of the mirror the
radius of curvature so it's from the
face of the mirror out to the to where
the center would be and then halfway in
between so this is one-half of the
radius you get to F the focal point and
the focal length would be the length
associated with going from the mirror
out to that location in space which is
also half the radius so those are those
two locations C and F okay so this is
going to be case one here's my object
I'm really only going to draw two
different rays to do this the first ray
goes in parallel so that's my attempt to
draw a parallel and then it's going to
reflect out angle N equals angle out off
this curved mirror and it's always going
to go through the focal okay so it goes
through F right there here's C so that's
my first ray the next one goes in
through the focal so it goes like that
and then it reflects out parallel to the
principal axis so what I get from this
is I get my brand new image right there
and I can say that for case one the
image is located between C and F it is
inverted because it's upside down given
that it's inverted that makes it a real
image I would be able to actually
project that image onto a piece of paper
and it also is smaller than the original
object so it would have a magnification
that is less than 1 or in between 0 and
1 making it smaller we would also tag
that magnification though with a
negative sign to indicate that it's
inverted it's case 1 by the way for this
first one I'll just mention that you do
of course have all these other possible
rays so there's one that goes out here
and it's going to go through that same
spot there's a ray that's going to go
here and it's going to go through that
Arrowhead there are an infinite number
of rays that I could draw it's just that
notice that this ray does not go through
the focal point this ray did not go
through the focal point the only ones
that are going to go through the focal
point are the ones that come in parallel
so that was this original red one
that'll go through the focal and then
the one that I went in with the green I
went in first through the focal will
leave parallel so on all these cases I'm
just focusing on the easy rays to do the
easy rays to draw are the ones that have
some sort of parallel to the principal
axis associated with them all right
let's do case two so here's my object my
little arrow just the simplest object we
can conceive of and I have two rays that
I'm going to draw first is in parallel
and out through the focal then I'm going
to have in through the focal and out
parallel now my picture is not you know
given that I'm not using a straightedge
for this you'll have to forgive me that
that's not perfect but what we get in
this particular case an image so my
image is always down here right I'm
using blue for my image my image is the
exact same size so it has a
magnification of actually negative one
because it's inverted which makes it a
real image and it is located at the same
position as the object so it's actually
located at C the center curvature that
is case two maybe I'll put what case I'm
working on up here as I go case three
I'm going to have my arrow hanging out
in between C and F whenever you draw
these don't put it too close over here
it causes problems because it would get
pushed way far out way far beyond the
page but let's go ahead and do my ray
diagram so in parallel out through the
focal then I'm going to have in through
the focal and out parallel and where
this is supposed to be and so maybe I
should have moved it in even a little
bit more than I was saying my object
this is getting larger it's now bigger
at a larger arrow it's outside of C okay
there see it's further out than C it's
still a real image and it's inverted let
me show you what would happen had I put
my object there notice that the red
would be the exact same there would be
no difference whatsoever in the red so
my red would continue on going out that
way but when I would go in to make my
green one and this time I'm going to use
blue real quick just to keep it separate
it would go way far down and be way down
here somewhere and then it would go out
and so it would be huge
big ol image that's out there but it is
actually nice to notice that that red
one would be the same case for is a
situation where I have my object located
on F and this immediately poses a
problem for me given that both the
center and curvature and the focal point
are both single points in space it
really is kind of impossible for me to
have a two-dimensional or even a
three-dimensional object located
entirely on F there's not a whole lot we
can do to resolve that what we do I
suppose is let's go ahead and say that I
have just the tiniest of all possible
little arrows that's totally located
entirely on F what I'll do is I'll show
a ray that's going to go through both
the arrowhead and through the focal it's
going to travel in and so I guess it has
to reflect out parallel I could draw
another one that goes in through this
direction it's still traveling through
the arrowhead and through the focal and
it will reflect out parallel I could do
an infinite number of rays that are
going to follow this this same pattern
and in doing so I make an observation no
matter what rays I collect over on this
side they are all parallel to one
another and so they will never actually
cross in case four we say that there is
no image because there's no image it
really doesn't make much sense for us to
talk about things like is the image
upright or inverted we simply just leave
it at that
there is no image that can actually
happen when an object is located on the
focal point if you do this in practice
what it means is that things are just
blurry so you'll still get light that
comes in and it's going to find its way
to your eyeball eventually but like I
said it just won't be a focused image
it'll just be very blurry the last of
these cases is another one that causes
some trouble with people because I'll go
in and put my red one here my red one is
going to go in
parallel and out through the focal so
that one's pretty easy that one looks
the same that it looked as if you know I
had maybe my my image or excuse me my
object way out there it really is the
same ray that would have gone through
the one that is funny is I go for my
green and I want to start up here and I
want to make my way through the focal
the problem is is that I won't run into
the mirror if I treat it like this I'm
going to head off into a different
direction and so all you really have to
do is you just have to conceptually say
well I just kind of need to get the Ray
that is on that line and really it's
going to cross through the focal first
and then out parallel so it looks like
that my red one had a ray right here
alright so I put the arrow heads on the
reflected Ray's what we need to do is we
need to trace back beyond the reflected
Ray's that means I trace back on that
reflected ray and I trace back on that
reflected ray and I find that I have an
image those light rays are allowed to
converge it's just that they don't
converge on this side of the mirror you
can see those things are never going to
meet up again where they can converge
this behind the mirror so that by
definition is a virtual image back here
so we have a virtual image it's upright
it is bigger so it has a magnification
that's greater than one and we just kind
of say it's behind the mirror and then
our last is case convex so there's
really only one way that we can talk
about a convex ray diagram it only has
one particular case for it so I still
have my focal point back here I have my
Center curvature back there
remember the focal length would be
negative I just kind of want to
reinforce that everywhere I can
that because it's behind the mirror we
have to tag it with a negative sign when
I have to use my mirror equation which
I'll do on a different review video but
let's just look at the ray diagram so I
go in parallel just like before and I go
out through the focal well out through
the focal would send me into the mirror
which is not something that can happen
in real life
but I need to take that path so I'm
going to trace up and it's going to go
that way you could see that I would
still have a nice pretty law of
reflection angle in theta is equal to
angle out theta all that good business
there but so that's my first ray diagram
the next one goes in through the focal
so it's going to go this way and if I
could continue on I would dot dot dot go
through the focal I'm going to erase
those dots though for a moment because I
don't want to cause confusion on
something but then I'm going to reflect
out and now when I need to find where my
image is going to be located I always
need to go back behind the reflected one
so that's going to send me off of that
go in and I draw my image here I have a
little arrow it's hanging out right
there it is a virtual image it's behind
the mirror so it's a virtual image it is
upright and it is smaller so that would
have a magnification that's positive but
it would be between 0 and 1 all right
hope everybody remembers those ok I will
be asking you to draw a couple of those
for me so if you think you got to figure
it out let your computer know