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In this lab, we'll take a look at how we can use systems of lenses: to look at distant
objects through a telescope, look close-up at objects with a microscope, or to correct
the focusing of the human eye.
But before we even think about multi-lens systems, we'll have to really understand single
lenses-- what do they do, and how do we use them to make real or virtual images of an
object?
A converging lens will take light from an object at infinity and focus it down to a
point, one focal length away. When this happens, we say that we've made a real image of the
object at that point, since all the light from the object really does pass through that
point. In fact, if we place a screen there we can see a little picture of the object
out at infinity.
If our object is closer to the lens, then the rays of light from the object are diverging
more at the lens than they were when the object was at infinity. The lens bends the light
and the rays focus farther away than the focal point. We've still got a real image since
the rays really do intersect.
When the object is brought to the focal point of the lens, the lens can bend the light just
enough to come out parallel on the other side. Since the rays don't really intersect anymore,
we could either say we have a real image at infinity, or a virtual image at negative infinity.
If we bring the object even closer to the lens, so that it's now inside the focal length,
the light rays from the object are diverging too much for the lens to focus, and the rays
continue diverging after they've passed through the lens. If the object is close to the focal
point, the rays will be just slightly diverging, and will look like they're coming from a point
far behind the actual object. We then say the lens made a virtual image out at that
point. It's virtual, in this case, because the light never really came through that point.
So we couldn't put a screen or some camera film anywhere to see the object.
We CAN see it with our eye though-- since our eye can collect diverging rays of light
and focus them onto our retina,
and this is exactly what we're doing when we use a magnifying glass. We're putting an
object near the focal point of a lens, and our eye is looking at the magnified, virtual
image out in the distance.
If we're using a magnifying glass to look at an ant, we're looking at rays of light
coming from a real object-- but we could use the magnifying glass in the exact same way
to look at rays of light coming from a real image formed by a second lens. We'll do this
when we look at telescopes-- we'll use a magnifying lens (the eyepiece) to look at the image of
a far away object made at the focal point of an objective lens; and we'll do it again
when we look at microscopes-- we'll use a magnifying lens to inspect the real image
formed behind the focal point of our objective lens, of an object close to the objective's
focal point.
This is, in general, how lenses combine-- the image formed by one lens in a system becomes
the object for the next lens. We'll see this one more time in the last part of the lab--
the image formed by corrective lenses will become the object for the lens inside a model
of the human eye.
To examine a converging lens, try putting the lens and a screen on rails and aiming
it out the window.
The red-labeled lens has the shortest focal length, so it'll be the easiest to use to
get a bright image.
If it's a bright enough day outside, you can use the building across the street as your
object at infinity.
If you have the screen about a focal length away from the lens, you'll be able to see
the inverted image of the building outside focused on the screen.
You can replace the red-labeled lens with a green-labeled lens with a larger focal length
to see an image with higher magnification.
To measure the focal length of a lens, this is what we'll use. We'll place a light source
at the zero-mark on our set of rails, and a screen 30cm away.
We'll measure the focal length of the red lens by using it to form an image of the light
source on the screen. Slide the lens back and forth and note when we have an image in
focus in the screen. From these values we'll be able to calculate the focal length of the
lens.
When we move on to telescopes, we'll use the long focal length lens as our objective lens
and the shorter focal length as our eyepiece. Point the setup outside at an object far away.
If you look through the objective lens, you'll see the object inverted.
If you look through both lenses together, you'll see the image is still inverted, and
now magnified.
Lastly, here's our model of the human eye. There are slots for lenses on the outside
which we'll use to model external corrective lenses.
The inside is filled with distilled water to model the vitreous, and slots for lenses
at the front of the eye represent different positions of the eye's crystalline lens. The
screen at the back is the model's retina, and it's movable away from or toward the lenses,
which we'll use to model near-or far-sightedness.
If you point the eye model at a bright object, you can adjust the lenses to achieve an image
in focus on the retina.