Mirror optics

could you illustrate in order that I can understand what you are talking about?

Sorry, there is no illustration possbile, I am trying to envisage a possibility. Take a convex mirror of an surface area S, whose base curve is +d.. Make a matrix of cavities in that surface, whose power is -d (the exact power of the base curve of the mirror); th total surface area of the cavities is 1/2 of the total surface area of the mirror, such that the total surface area of the cavities equals the remaining surface area of the mirror.

So, the question is, since the remaining surface area of the +d equals the surface areas of the -d concave surfaces, and +d is the same power as -d, is the resultant power of the mirror, which should theoretically be a composite power, equal the sum of +d-d?

The answer is no. The convex surface will have the same power whether or not there is an array of cavities. Each cavity will act as a separate mirror, not as a continuum because the mirrors do not align on the same concave curve.

The net result will be that you will have a continuous mirror of power +d, speckled with many tiny mirrors of power -d.

Thanks for the thoughts.

At the next level, each of the concave lenses generating a reflection image, and the remaining interconnected convex surfaces also generating a reflection image, will not there be constituted a standing wave of a composite image?

I still dont understand.

what is power? the curve equation's power?

f(x) , the power of x?, why +d-d cannt equal to zero?

anyone out there can sketch?

Hello cnpower

The concept is somewhat similar to multiple-lensed eyes, such as bees and other insects use.

The difference is the surface is concave, not convex.

The reflector is a mirror surface, not a lens which transmits light.

The analogy is poor, and I hope you see the similarity, also the differences between the multi-faceted mirror and the multi-faceted eye lens.

Kind Regards....

but what is +d -d?

it seems very complex issue.

ah, forget it.

What you have here is a bi-focal mirror. Assuming that the concave sections are parabolic, they will create an image (of an object at infinity) at a distance of 1 meter in front of the mirror. The convex portion will create a distorted 'image' that appears to be 1 meter behind the mirror.

Thanks for your cogent reply.

Yes, each of the concave lenses will generate an image, and the remaining interconnected convex surfaces will also generate an image.

Will not this cause a standing wave image to be generated, a composite image?

This does occur in multifocal optics when the focal planes are close together. For example, if the 'base' curve is 1 Diopter, and the second curve is 1.1 diopter, the two images will be close enough together that an observer focusing on one image will be distracted by the slightly defocused second image. This can result in interference, but the interference is due to the structure of the defocused image (which is an image of some particular object with specific spatial qualities) adding and subtracting to the focused image.

When the images are far apart as in the original example (+1 and -1), then an observer focused on one image will not see any structure in the defocused image, and will merely perceive it as stray light or veiling glare.

No. By asking the question I think you are misunderstanding several different concepts. As you have already been told twice, you will get a bunch of little focused spots and you will get a really screwed up defocused one equal to a focus behind the mirror. No standing waves. No composite image. Period.

A composite image is a combination of many images into one and is mostly used in computer speak for manipulating many photos into a single combined image to achieve some desired effect. In your case, the images created at the focal points of the dimples and the main mirror surface would somehow have to all be combined together at a single focus at a single point in space to form a composite image. By the very definition of your "optic" that is absolutely impossible - even for just the litte spots from the dimples.

In order to have standing waves, you would need an optical cavity or at least a waveguide with partially reflective ends and with your mirror as one end. The standing wave comes from having a wave traveling each direction (reflected back and forth) combining to form a single "standing wave" of nodes and anti-nodes with a wavelength to appropriately match the cavity length because the light is of exactly the right frequency for that cavity length. Even if you had a second mirror to try to create standing waves (for what reason I know not), it would not work with your defined optic except possibly off the very center, but only at that point and assuming it is either a part of the mirror without one of your dimples or is the exact center of one of the dimples.

To summarize, no standing waves and no composite image.

Hello PhysicsProf

As the number of dimples became infinite, and the depth of each became correspondingly shallow, a perfect mirror would result.

Kind Regards....

Hello Sparkstation,

If the number of dimples becomes infinite, wouldn't you wind up with a convex mirror? Each dimple may be shallow, but the overall configuration of the curve is convex with a curvature of +d (whatever that means). So maybe what you are saying is a perfectly convex mirror would result...right?

That was not the problem as stated. Even still, no composite image, just a reflection and no standing waves. In your case we simply end up with one focal point.