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In
this section, we look at some of the properties of ideal lenses and
mirrors. The level is pretty simple throughout; little more
than
basic trigonometry is assumed. None the less some of the
results
get rather complex.
In this section, we're going to assume
that lenses and mirrors form images, and then look at some of the
details of the image formation. Elsewhere, we proved that
parabolic mirrors bring light to a focus.
A proof that a parabolic lens brings light to a focus would be a
bit more complex, as lenses are not quite so simple as mirrors, but
geometrically very similar. In no case do we attempt to prove
that parabolic mirrors or lenses actually form perfect images -- as, in
fact, they don't. We discuss this in a little more detail
when we consider ideal lenses and mirrors.
| A
discussion of what we mean by an "ideal" lens or mirror, along with
some notes on how they differ from real lenses and mirrors. |
Ideal
Lenses and Mirrors |
| A discussion of
images formed by lenses and mirrors: whether they're real or
virtual, how large they are, and where they're formed. |
Lens and Mirror Images |
| We
determine the brightness of the image formed in a simple camera.
This result is needed for some other things we'll do later. |
Camera Image
Brightness |
| It's
impossible to build a telescope, pair of binoculars, or other optical
instrument out of simple mirrors and lenses which makes extended
objects appear brighter. In other words, nebulae will
always appear dim when viewed through an ordinary telescope. |
Visual
Image Brightness |
Snell's law tells us how light bends as it
enters a piece of glass, or, more generally, moves between any two
dissimilar materials. We'll need it when we discuss real lenses.
|
Snell's Law
|
| Our initial model of an
ideal lens was incomplete. On this page we'll
determine exactly how ideal lenses bend light arriving at any angle. |
Ideal Lenses
Part II |
It's useful to give the
focal lengths of lenses in diopters
because when we stack two lenses, the resulting "combined lens" has the
focal length, in diopters, which is the sum of the focal lengths of the
two lenses in the stack.
|
Diopters and
Stacked Lenses
|
On this page we find the focal length of a
spherical lens as a function of distance from its center, and as a
function of its radius of curvature and the refractive index of the
lens material. Along
the way, we show that spherical lenses do not bring parallel
rays to a unique focus.
|
Spherical Lenses
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| On this page, we find the approximate
focal length of any tiny symmetric lens,
and show that tiny lenses act like ideal lenses for distant scenes
regardless of the "figure" of the lens surface. |
Tiny Convex Lenses
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What's the focal length of a parabolic
lens? It turns out that it hasn't got one -- any more than a
spherical lens has. We shall prove that, and find its approximate
focal length.
|
Parabolic Lenses
Not done yet
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Page created on 9/23/07. Last updated on
1/17/09. |
