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Showing posts with the label Spatial coherence

Is 0.999... = 1? (spoiler alert: no it is not)

You may have encountered the popular claim that \( 0.999... = 1 \), where the three dots signify that the decimal continues forever. This is a somewhat weird claim, since it would mean that mathematics is broken. There should be no way for two different numbers to have the same value. What makes it weirder is that this is quite popular claim. I've even seen mathematicians say that it's true! But is it though? One popular proof is to first denote \( S = 0.999...\) and then multiply by \(10\) to get \( 10S = 9.999...\) and subtract \( S \) from it, to get  \( 10S - S = 9.000...\) and finally dividing by \(9\) yields  \( S = 1.000... = 1 \) and we see that  \(0.999... = 1\)! However, there's a problem. This short derivation is not strictly speaking correct. It is veeeery close to being correct, and to see why let's look at finite decimals first. Let's say that \(S = 0.999\) (note that this is not the same as \(S = 0.999...\) ). Let's do the same trick as ...

Is it possible to make a laser out of wood?

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Wood is a precious material. It has been used for thousands of years as fuel, in construction, for tools and weapons, as well as for furniture and paper. It is also important for biochemistry in the production of purified cellulose and its derivatives, such as cellophane and cellulose acetate. Wood has unarguably been the most important raw material that allowed civilizations to flourish and it will probably remain that way. But quite recently the usefulness of wood has expanded to a completely new area: photonics and optics. When you think about it, it sounds improbable, or even down right stupid to use wood as a material in optical physics, but that's really what has been going on! Let me be clear, this is not the type of wood you would traditionally use, but chemically treated so that it transmits light. The process is simple in principle, you just soak some wood in a chemical that dissolves lignin. Then you take the delignified wood and add epoxy to it, and voila! You...

Update on the double-slit experiment

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After two papers on something that I did not receive an education for, I finally got a topic in photonics, my bread and butter to be. I started working as a part of the coherence coherence group of UEF in the summer of 2015 and my first task was to design and build an interferometer, which would be used to quantify spatial coherence. Thin film interference. Physics is pretty, ain't it? Now, one might ask, what is spatial coherence? The idea behind this concept is simple: it describes how well different parts from a beams cross-section correlate with each other. If the correlation is strong, then we talk about high coherence and low when the correlations are weak. A very good overview of spatial coherence and its measurement can be found  here . The usual way to measure it is to use the  Young's interferometer  (a double slit experiment, variations of this are used in quantum mechanics), but there are some problems. First of all, a single measurement is not eno...