Video Transcript
Which of the following statements correctly defines what is meant by the term “coherent light”? (A) Two or more light waves are coherent if they have the same frequency. (B) Two or more light waves are coherent if they have a constant phase difference. (C) Two or more light waves are coherent if they have the same frequency and amplitude. (D) Two or more light waves are coherent if they have the same amplitude and a constant phase difference. Or (E) two or more light waves are coherent if they have the same frequency and a constant phase difference.
Between all of these answers, it seems that we are given three different properties through which to judge if two or more light waves will be coherent, which are if they have the same frequency, if they have a constant phase difference, and if they have the same amplitude. Let’s look at each of these, starting from the bottom with amplitude. Amplitude is the height of a wave and is measured using the highest or lowest points of the wave, the peaks or valleys. Amplitude does not have an effect on the coherency of waves, even if the difference in amplitude between the waves is quite large.
Because answers (C) and (D) both mentioned having the same amplitude, we know that they cannot be correct. So let’s remove them entirely to make some space so we can look at frequency. The frequency of a wave is how frequently it oscillates as it travels forwards. A wave with more oscillations over the same period of time has a higher frequency than a wave with fewer oscillations, which would have a lower frequency. In order for two or more light waves to be coherent, it is necessary for them to have the same frequency. So these two light waves, for example, are not coherent. But these two are because they have the same frequency and indeed are the same wave. Since answer (B) does not mention frequency at all, it is incorrect and we can remove it.
Now, we know that the waves must have the same frequency. But what if they have a different phase, something like this perhaps? Well, we know these waves still have the same frequency since over the same length, they are both covering one complete wave cycle. But for determining coherency, what matters is not the phase, but rather the phase difference and specifically a constant phase difference. And to discuss what a constant phase difference is, let’s recall the phase in degrees of points on a typical sine wave.
The start of a wave is zero degrees, peaks are 90, midpoints on a wave halfway down are 180, valleys are 270, and the ends of waves are 360 or zero degrees, since the end of a wave is the start of a new one. Using these measurements for phase, we see that the top light wave starts at 90 degrees and the bottom one starts at zero degrees. If we now look at all of the other points on these waves, we’ll see that the phase difference between any two points that occur at the same time is 90 degrees. Note that whenever we use the value of phase that could be either 360 or zero degrees, we use the one that would ensure that we get a positive answer.
Now for these two waves, we see that there is a phase difference between them that is constant at all points. And a constant phase difference of 90 degrees between these two waves with the same frequency means that they are coherent. If, however, we add a third wave with the same phase as the third wave, then we cannot say that all three of these light waves are coherent with each other because while they all do share the same frequency, they do not share a constant phase difference between all three of them.
We already saw that these two waves have a constant phase difference of 90 degrees. But these two waves, since they have the same phase, have a phase difference of zero degrees, which means that the phase difference changes between which two waves we’re measuring, which means that these three waves do not have a constant phase difference. If we’re only looking at two waves and they have the same frequency, then it usually means they also have a constant phase difference. So it doesn’t seem so necessary, but when we are looking at three or more waves, it very much is necessary. So only looking at the frequency, as answer (A) suggests, is not correct.
The statement that correctly defines what is meant by the term “coherent light” is answer (E): two or more light waves are coherent if they have the same frequency and a constant phase difference.
