INTENSITY LIGHT EQUATION KH SERIES

If the pit is taken to be a quarter-wavelength in depth, then the light reflected from the pit is half-a-wavelength out of phase with the light from the land, resulting in destructive interference and less light at the detector:īut, as noted, the light doesn’t get “canceled” completely it just goes somewhere else.

When a ‘pit’ is present, however, the focused beam partly reflects from land and partly from pit. Light illuminating ‘land’ gets directly reflected and collected at the detector. The modulation of light is caused by interference. Part of the back-reflected light gets directed by the splitter to the detector, and the absence or presence of light at the detector registers as a ‘1’ bit or ‘0’ bit. Light from a laser passes through a beam splitter and is focused by a lens onto the disc. The disc is read by focusing light onto the surface, and measuring the amount of light reflected back, as crudely illustrated below:

INTENSITY LIGHT EQUATION KH SERIES

The data on a compact disc is encoded in a series of ‘pits’ surrounded by ‘land’, which correspond to a ‘0’ or ‘1’ bit. This observation - that interference redirects light, and doesn’t cancel it - actually plays a role in the operation of compact disc players. It can be shown, however, using some straightforward mathematics, that the total light collected on the measurement screen B is equal to the total light that passes through the two holes: interference affects where the light goes, but not how much of it there is in total. The presence of interference means that more light shows up in some places and less light shows up in other places. Light emanating from the two slits in the screen A produces an interference pattern on the measurement screen B, a simulation of which is shown below: The perfect illustration of this is Young’s double slit experiment, which I have discussed before: In general, we can say that the interference of waves doesn’t “cancel” energy, it just moves it somewhere else.

Waves in a one-dimensional problem like a vibrating string are a bit of a special case however, a similar argument can be made for higher-dimensional problems. There is no “energy cancellation” involved. The proper interpretation is that the second excitation in the center of the string actually adds no energy to the string at all! In fact, the second excitation on the string just blocks and reflects the first wave. Looking at the picture, though, the actual physical result of our two excitations is that the first wave, propagating to the right, is reflected back to the left! There is complete destructive interference to the right of the second excitation. What does the situation look like when both waves are applied to the string at the same time? We have: Individually, the first wave is propagating entirely to the right the second wave spreads out in both directions from the point of application. The second wave is generated locally at a point on the string by some sort of applied force:

Let us formulate the problem as follows: one wave is generated far away on the left of the string, perhaps by a hand shaking it up and down. The first of these is the observation that the answer to the question depends on how the waves were generated in the first place!

There are actually two aspects to the answer that I want to address, each of which is rather important in the understanding of wave phenomena. My student asked me: what happens to the energy? As posed, it seems that we started with two waves carrying energy, but they canceled each other out, leaving no energy! This interpretation cannot possibly be correct, so where is the flaw in our description? The two waves cancel each other out, leaving a completely unmoving string due to destructive interference. Now suppose we excite the string with an additional wave of the same frequency and amplitude, but completely out of phase. This wave carries energy, and there is a net flow of energy to the right. The situation in question is as follows: suppose you have a harmonic wave on a string traveling to the right such that in a snapshot of time, the string looks as follows: It’s really nice to get a question that indicates a genuine interest in the science (as opposed to just wanting an answer to homework), and I thought I’d discuss the question and its answer as a post. Last week was a relatively lousy one for me, but it was made up in part by getting a good question from a student on waves and interference after class.

Intensity light equation kh