Do not attempt to adjust your screen.
I'll do it for you.
There, that's better.
What causes a blurry image,
and what can we do to fix them?
We'll found out how optics can help us see better
and do more
in this segment on spherical lenses.
♪♪
Lenses are everywhere.
In anything that has eyes.
In microscopes and cameras,
telescopes, magnifying glasses,
as well as car headlights.
A lens is any transparent material
with a curved surface.
Even a droplet of water.
There is one particularly amazing kind of lens
that can do some things better
than any other kind of lens.
Any idea? No?
It's the lens in your eye,
which is capable of changing focus from the micro
to the macro,
literally in the time it takes to blink.
That's an incredible miracle of evolution.
No other lens has the flexibility
and response time.
Your eyes can do this
because they have flexible lenses
controlled by muscles.
They can bulge in and out,
changing shape in an instant
to focus on what you're looking at.
Let's see what else lenses do,
and how they affect light rays,
and consequently, what we see.
Here's what happens when a light hits a lens.
Rays from a common point source,
like a light bulb, refract,
and they are bent,
which changes their direction.
They may be bent so that they converge,
like this,
or diverge, like this,
where they are refracted outward
away from each other
or in many different directions.
Whether they converge or diverge
depends on the shape of the lens.
As we discussed in another segment,
there are two main kinds of lens shapes.
The first one we'll look at,
or through, is a convex lens,
which means it curves outward.
Convex lenses are converging lenses.
This means the light rays come together at a point.
As they emerge from the lens, they converge.
Convex lenses are used in things like telescopes
to bring distant light rays
to a focus in your eyes.
The second type is the concave lens.
That's a lens which curves inward,
and we are particularly interested in biconcave lenses
that are curved inwards on both sides.
Look at the shape of the lens
and imagine rays of light hitting it.
What do you think happens to them?
They diverge, or spread out.
We'll talk about how the curved surfaces
affect the images we see in a minute.
But before we do that,
let me explain a few important terms
which will help us understand
how the optics of spherical lenses work.
First, let's talk about the center of curvature.
Think of a spherical lens as a part of a sphere.
It's like a section that has been cut out.
The center of curvature is the point in the center
of the imaginary sphere from which the lens is cut,
whether it's a convex or concave lens.
Now let's talk about the principle axis.
The principle axis is the horizontal line
that connects the center of the spherical lens
with the center of the imaginary sphere.
The next term, focal point,
is simply the point where converging
and diverging lenses focus light.
The better the lens,
the more light rays converge at the same focal point
and the clearer the image.
There is a formula for the focal point.
It's equal to half the distance
from the center of the lens at the principal axis
to the center of curvature.
When light rays hit a refracting surface,
they can create one of two kinds of images,
depending on the curve of the lens
and the location of the object.
Convex lenses, for instance,
can form a kind of image called a real image,
which appears when light rays converge in real space.
You also know it's a real image
because it can be projected onto a surface.
One example of a real image
is what you see on a movie screen.
You can make a few different sizes of real images
with convex lenses,
which is what we're gonna do in a moment.
The size of the image we'll see
depends on the distance between the object
and the lens.
But first, let's look at a diagram
of one of these real images
so you can see what's happening.
Let's analyze one form by an object
beyond the center of curvature.
You can predict the position of the image
by creating a ray diagram
of just three representative rays.
We'll use a biconvex lens
which curves out on both sides.
See the O on the principle axis
in the center of the lens?
That's the optical center of the lens.
Let's draw a light ray that is parallel
to the principle axis.
When it strikes the lens, it will refract
and go through the focal point,
which is on the side of the lens
opposite the object.
Now let's draw a second ray.
It goes right through the optical center
so it does not get refracted or bent.
It continues in a straight line.
Finally, we'll draw a third ray
that goes from the object
through the focal point on the same side of the lens
as the object and strikes the lens.
After it hits the lens, it will refract horizontally
to the principle axis.
The point at which the red lines cross
is where the image will be in focus,
so since it's a real image, it will be inverted
below the principle axis.
Wanna see that in real life?
I have a convex lens and a blackboard.
Plus I have this LED light
that we'll use as our object.
The light has two green bulbs
and a single blue bulb on top.
I have the light here,
and I hold up the board.
Now when I hold up the lens...
we see the color image of the light.
And since our lens is one dimensional,
so is the image.
The image is real
since we can project it onto a surface.
Notice that blue light is now below the green light,
that the image is upside down,
inverted,
and smaller than the actual object.
I'm gonna move the lens closer to the light,
and let's see what happens to the image.
It got bigger, see?
It's the same size as the actual object,
but still inverted.
That's because the image has moved further away
from the lens,
so that the light is converging
a longer distance from the principle axis.
Now I'm going to move the lens even closer to the light,
between the center of curvature and the focal point.
Now look at the image. Magnified, right?
Why do you think that is?
It's because the refracted rays converge at a place
even further below the principle axis.
Now what if the light is at
the focal point of the lens?
What kind of image would we get?
Um, that's kind of a trick question.
Because the answer is none.
That's because the refracted rays
travel parallel to one another,
and never converge with one another.
Next, let's move our lens so that the light
is inside the focal length.
A virtual image is one where light only appears
to converge on the surface of the lens.
It's actually converging in front of the lens.
Virtual images, unlike real images,
cannot be projected onto a surface.
You can see how virtual images are formed
in this ray diagram.
Virtual images are right side up
and magnified.
This is how magnifying glasses work.
They are basically convex lenses,
so it creates a magnified virtual image
that allows you to see objects
in greater detail.
Virtual images are also formed
by another kind of spherical lens,
concave lenses.
In fact, all images produced by concave lenses
are virtual.
The image is smaller in the lens than the real object.
Now watch as the object moves closer to the lens.
The image gets bigger,
but not ever as large as the object.
This image is always smaller than the object
because the refracted rays converge at a point
in the lens closer to the principle axis.
Lenses are incredibly useful and adaptable.
They can help us see farther,
or better, or bigger,
or smaller.
Here's one of the most powerful telephoto lenses made.
Look at what it can do,
keeping the image in focus from amazing distances.
Lenses have become a part of our daily lives,
as well as indispensable in science and industry.
Optics open up a whole world of fascinating careers,
so take a good look,
and if you want to know more about the mathematics of lenses,
check out the Closer Look.
It will show you how to use the Lensmakers Equation,
which calculates the focal length of a lens,
or distance to an object or image.
It also covers the equations for finding
the magnification of a lens.
That's it for this segment of "Physics in Motion."
We'll see you next time.
(announcer) For more practice problems,
lab activities, and note taking guides,
check out the Physics in Motion toolkit.