Linearly polarised lightformula

When you remove all the interior of a lens like the one above, you end up with a flat piece of material with many concentric grooves in it, as shown below.

The grooved side should face the sun if you want the maximum effect. As the following diagram shows, if the flat side is facing the sun then not all the light meets at the focal point. This is something I actually verified experimentally. With my fresnel lens solar cooker, it took 2.4 times as long to bring 150ml of water from 40C to 60C when the flat side was facing the sun compared to when the grooved side was.

Linearly polarised lightmeaning

A fresnel lens is just a lens like one below, but without all the interior material, which is not needed for a lens to function.

The following is a video I made showing much of the above, including the experiments I performed to verify some of it. Enjoy!

Circular polarization

It turned out that the fresnel lens which I got from a rear projection TV and used for my solar cooker produces a short line at the focal length about 2 to 3 inches long and about a half inch thick at its thickest. However, my magnifying glass fresnel lens produces a sharp point, or spot, at its focal point.

Making a fresnel lens that doesn't suffer from spherical aberration is simply a matter of making the grooves less steep by appropriate amounts. This is easy to do since it means just cutting the grooves differently than they otherwise would have been. The resulting lens is referred to as an aspherical lens.

But there's still the problem of spherical aberration. Spherical aberration, as the diagram below shows, is when not all of the light meets at the focal point. This happens with lenses that are derived from spheres.

Light can be described as an electromagnetic wave traveling through space. For purposes of ellipsometry, it is adequate to discuss the waves’s electric field behavior in space and time, also known as polarization. The electric field of a wave is always orthogonal to the propagation direction. Therefore, a wave traveling along the z-direction can be described by its x- and y- components. When the light has completely random orientation and phase, it is considered unpolarized. For ellipsometry, however, we are interested in the kind of electric field that follows a specific path and traces out a distinct shape at any point. This is known as polarized light. When two orthogonal light waves are in-phase, the resulting light will be linearly polarized. The relative amplitudes determine the resulting orientation. If the orthogonal waves are 90° out-of-phase and equal in amplitude, the resultant light is circularly polarized. The most common polarization is “elliptical”, one that combines orthogonal waves of arbitrary amplitude and phase. This is where ellipsometry gets its name.