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Simple Optical Properties of Lenses and Mirrors

Proof by Picture
basic stuff
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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
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
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
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

Page created on 9/23/07.  Last updated on 1/17/09.