Skulls in the Stars

How do we define how fast a wave is going? The question at first glance seems obvious. When we discussed harmonic waves in a previous post, we observed that the velocity of the wave could be measured by measuring how far one of the peaks of the wave travels in a certain amount of time. There are a number of subtle points that arise when talking about wave velocity, however, including the possibility of light traveling at faster than the ’speed of light’! In this post we’ll try and define the velocity of a wave, and explain why the question is not so easy to answer.

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To conclude my discussion of optics basics, I want to introduce some of the standard quantities used to describe waves and wave propagation. Unlike previous ‘basics’ posts, this one will necessarily deal with a little bit of algebra and perhaps a little trigonometry.

The simplest wave to deal with from a theoretical point of view is a harmonic wave, one which consists of an infinite sequence of regularly spaced ‘ups and downs’. A portion of such a wave traveling to the right on an extremely long string would appear as:

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In part II of my series on ‘What is a wave?’, I addressed one of the two most significant behaviors of waves, namely interference, the ability of a wave to ‘interact’ with itself. The second behavior of waves which is extremely significant is diffraction, and we will address it in this post.

Diffraction may be broadly defined as the tendency of a wave traveling in two or more dimensions to spread out as it propagates. The most significant consequence of this spreading is the ability of waves to ‘bend around corners’ when faced with an obstacle. We all have experienced the diffraction of sound waves: if you and a friend stand on opposite sides of a large building (say a farmhouse) in the middle of an open field, you will be able to talk to each other even though there is no direct ‘line of sight’ between you and your friend, and no ability for the sound waves to reflect off of intermediate surfaces. The sound waves wrap around (diffract around) the outside of the farmhouse, allowing communication.

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In the first part of my series on ‘What is a wave?’, I attempted to give a broad definition of a wave, so that we can identify them when we see them. In this part, I will address two of the most important behaviors of waves: interference and diffraction. Interference may be loosely described as the interaction of a wave with itself, or a wave with another wave, while diffraction may be loosely described as the interaction of a wave with other objects.

We will discuss interference in this post, and consider again the wave on a string discussed in part I of this post. A pair of waves are sent down the string to a fixed end, where they are reflected and return to their point of origin. What happens when the waves pass each other? An animation of such an event is displayed below:

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As I’ve mentioned a number of times before, my optics specialty is physical optics, which is the study of the wave properties of light. In order to understand those wave properties, however, it is important to understand what a ‘wave’ is and what it can do. This article is an attempt to answer these questions in a non-technical way for the layperson.

This is not as easy to do as one might think. Most of us are aware of numerous wave phenomena: waves on a string (such as a guitar string), water waves, sound waves (acoustical waves), seismic waves (earthquakes), ‘The Wave’ at football games. There are also many less familiar examples: light waves, particle waves (quantum mechanics), gravitational waves (caused by collapsing stars, for instance). It is quite difficult, however, to explain what these phenomena have in common. Furthermore, as we will see, any definition of a ‘wave’ that we come up with will have exceptions. I suspect most physicists would give a definition of a wave that’s similar to the Potter Stewart definition of hard-core pornography: “I know it when I see it.” We will do the best we can, though, and note those exceptions as they arise.

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Since this is supposed to be in large part a science-focused blog, I wanted to get started with some serious posts about scientific topics. Like most of the established science bloggers, I’ll be mixing up posts which are on basic scientific concepts and posts which are on specific, technical, topics. This post will be one of the former.

My physics specialization and area of research is optical science. Though most people associate the word ‘optics’ with the engineering of lenses for eyeglasses, telescopes, and microscopes, in physics the term more broadly refers to the study of the behavior of light and its interactions with matter. The connection to eyeglasses and the like is not accidental, however: the development of various optical tools led scientists to study more closely the behavior of the light that those tools channeled.

Today, we may roughly group the study of optics into three broad subfields of study:

1. Geometrical optics, the study of light as rays
2. Physical optics, the study of light as waves
3. Quantum optics, the study of light as particles

Let’s look at each of these subfields in turn, both historically and scientifically.

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