| Cylinders and compound lenses. Optical cross. Flat transposition. |
You will need a sphero-cylindrical lens for a demonstration at the end of this lesson. Call your instructor if you do not have access to lenses.
Up until now
we have been dealing with lenses having surfaces that are spherical.
That means the surfaces can be thought of as being a part of a sphere.
They had a radius of curvature: every point on a particular surface was
the exact same distance from some point that was the center of the sphere
that created the surface.
All surfaces are not like a portion of a beach ball. Look at a can of
soda. In one direction the side of the can is completely flat, or plano.
In a different direction it has some curvature; exactly perpendicular to
the flat side it is circular.
Now look
at a donut. There are ways to cut this so that you have large circles,
medium circles, and small circles. In-between those circles are elongated
circles or ellipses. If we take just a portion of the surface of the donut
we will have a surface that is circular in one direction, circular but
of a different size exactly 90 degrees away from the first direction, and
curved but not circular in every other direction.
The surfaces that we were working with were spherical because they had one center of curvature, and had the same amount of curvature regardless of how they were cut. The surfaces of a can, which is a cylinder, or a donut or a football are not spherical. They are called toric. A toric surface has two circular curves 90 degrees apart, or perpendicular to each other. The rest of the curves in-between those 90 degrees are not circular.
Read through page (37-40 / 52-54) in Optical
Formulas Tutorial.
Press the BACK button at the top left of the screen to return to the assignment page.
