Image Formation by Convex Lens Video Lecture - Class 7

We've talked a
lot about mirrors,
in particular parabolic
mirrors, that reflect light.
What I want to do now
is talk about lenses,
or talk about what a lens is.
And think about how they
transmit or refract light.
So a simple lens, and
we've all seen them.
Maybe it's made of glass,
maybe something else.
And I'm going to focus
on convex lenses first.
So remember, concave means
it opens inward, like a cave.
Convex means it kind
of opens outward.
And in a convex lens,
it'll be symmetric.
So let me see if I can draw it.
One side of the lens
will look like that.
And this one, you could
kind of view this.
And oftentimes, most
lenses, the simpler lenses,
are made this way.
So this is kind of the
surface of a sphere,
or part of the
surface of a sphere.
Let me see if I can draw
that a little bit better.
So part of the surface of a
sphere, and it's symmetric.
So it has some center, right
over here, just like that.
And then you have
another surface
of a sphere that's
exactly the same.
I'm doing my best to draw this
convex lens, just like that.
That is a pretty good job here.
And let me copy and paste
it so I can actually
use this drawing in the
future, before I mark it up.
All right.
So I've copied it.
So let's think
about what's going
to happen as light
goes through this lens,
as it's transmitted
through it and maybe gets
diffracted by it.
So we're assuming this is air
out here, and this is glass.
Something that has a higher
index of refraction, something
in which light travels slower.
So you can imagine
that some light that
is going parallel-- I
guess you could view it
to the principal
axis of the lens.
This would be the principal
axis of the lens right here,
just like we talked
about the principal axis
of our parabolic mirrors.
But if you imagine light
that's going parallel to that,
right when it hits this
surface over here-- Remember,
the perpendicular
at this point is
going to look like this because
the lens is actually curved.
And remember, it's moving
faster on the outside.
So the right side is
going to be able to stay
outside a little bit longer.
Or actually I should
say, the top side
of the light-- if you
imagine the car analogy--
is going to be able to
stay out of the lens
a little bit longer
than the bottom side,
or the bottom wheels.
Or if we go in the
direction of the light,
the left side of the car
is going to be able to--
And just so we can visualize the
car, there's the left wheels.
Those are the right wheels.
The left wheels are going
to be able to stay out
a little bit longer and travel
faster a little bit longer.
So this is the
perpendicular again.
So it will it be
refracted downwards
like that, a little bit.
And then once you get
to this interface,
now you're going to move into
a faster medium, into the air
again.
And let me draw our
perpendicular over here.
And you could imagine that
the right side of this ray
is going to-- Actually,
the left side of this ray
is going to come out first.
And since the left side of
this ray, or the left side
of these tires are
going to come out first,
or maybe the top tires are
going to come out first,
they're going to be
able to travel faster.
And so you'll be deflected
even more downwards.
So it will look
something like this.
And the light ray would
do something like that.
Now there is a point
out here someplace
that whenever I take
any ray that is parallel
to the principal
axis of the lens,
it will be refracted through
the lens to that same point.
So here, we're going
to be refracted
a little bit like that.
And there we'll
be refracted more.
And then we're going to
go to that same point.
So that's another ray.
And then this is
another parallel ray.
It'll be refracted a
little bit over here,
and then a little bit more.
And it'll go to that same point.
And I think you could guess what
I'm about to call this point.
I wish I could draw my lines
a little bit straighter.
It's refracted a
little bit, and then
refracted a little bit more, and
goes straight into that point.
This point, where all of the
parallel rays-- Sometimes
you'll hear them talked
of as collimated rays.
Those are rays of light
that are roughly parallel.
They all converge at this point
on the other side of the lens.
They're essentially all
being focused on that point.
And this right here you can
view as the focus of the lens.
Or you can view this
length from the lens
to that point as
the focal length.
Now this lens is
completely symmetric.
Anything you can
do from one side,
you end up getting
focused on the right side.
If you had collimated
rays, or parallel rays,
coming from the right side,
the same thing would happen.
But it would just be
on the other side.
So that ray would go like that.
And then it would be
refracted some more.
And maybe it would go to
this point, right over here.
And so you actually have
two foci for a lens.
Two actual points where,
if parallel rays are coming
from one side,
they'll be focused
on the point on the other side.
And if parallel arrays are
coming from the left side,
they'll be focused
at the focal length
or at the focus point
on the right-hand side.
And this goes the
other way around.
Let me draw another lens.
And actually, one
thing that we're
going to assume while
we're dealing with lenses,
and this is kind of a
simplifying assumption,
is called a thin
lens assumption.
There is a difference
in distance
it travels, depending on where
the light travels in the lens.
For example, here there's
less distance than over here.
And in an introductory
physics-- and we're
going to do that
here, as well-- we're
just going to ignore that
difference in distance,
because that would lead to some
differences in how the light is
refracted and transmitted
and all of that.
Because it has to
travel a smaller
distance here than over here.
So we're going to ignore
those differences,
and we're just going to make
the thin lens assumption.
But using a thin
lens assumption,
let's think a little
bit about what's
going to happen with the light.
And in the next
few examples, I'm
not going to worry about
this kind of two-step.
I'm just going to say,
look, it just in general
gets refracted in that direction
when it exits the lens.
So let me just draw a
simple lens right over here.
It is symmetric.
And it has two focal
points, one on this side,
so that is one focal point.
And then it has another focal
point, the exact same distance,
on the other side.
This lens is symmetric.
So let's think about
what this lens will
do to the images of
different objects.
So let me draw its
principal axis again.
So both focal points lie
along that principal axis.
Now let's stick an object out
here, beyond the focal length.
So let's think about
what's going to happen.
So first, remember, we can
pick any point on this object.
Light is being diffusely
reflected off of every point.
I like to pick
points that are going
to do something that's
kind of predictable.
So let's pick a point.
Well, let's take the tip.
And take a ray that does
something that's predictable.
So let's take a ray that is
parallel to the principal axis.
I mean, I could
draw this two steps
so it gets refracted once.
And then it'll get
refracted again
through the focal point on
the other side of the lens.
So then it gets refracted
through there, just like that.
And then, I could
take another ray
from the tip of
that arrow that goes
through the focal
point on this side.
So it goes through the
focal point on this side.
And so that is going to
get refracted like this,
and then get refracted again.
So it comes out on the
other side of the lens,
going parallel.
And hopefully this
makes sense to you,
because it's kind
of a symmetric deal
that we're dealing
with over here.
Something coming in
parallel on the right side
will go through the focal point.
Then something going
through the focal point
will come out on the
other side parallel.
So whatever light is coming out
radially outward onto this side
and going through the lens
will converge at this point,
right over here, on the
other side of the lens.
And so you could do even
light that goes straight
through the lens would
end up right over there.
It actually won't
be refracted at all.
It'll just be able to go
straight through the lens.
And so the image
that gets formed
on the other side of the
lens will look like that.
So in this example,
it looks like we
have an inverted real image.
And once again,
it's a real image
because the light is actually
converging at that point.
You would actually be able
to put some type of a screen
and project the image there.
In the next video,
we're just going
to practice this idea of
drawing these rays to figure out
what type of images we'll get,
depending where the object is,
whether it's at the focal
point, beyond the focal point,
beyond two times
the focal point,
or within the focal point.
And the best thing
there is we'll just
get a lot of practice doing
this, drawing these rays
and thinking about how
they'll get refracted.