Many microwave ovens have a gauze in their window, to reflect the microwaves and keep them inside the oven. Someone once asked me “How come the microwaves can’t fit through the holes?”
It’s a brilliant question. Which we are not going to answer. If you want to, you can look up ‘how diffraction depends on wavelength’. And if the answer is obvious to you, you can carry on reading anyway, because the answer to the question is not what this post is about!
Instead, I think what is even more interesting is the thought pattern that led my friend to ask the question in the first place. Because in asking the question, he was visualising a microwave being something it isn’t… Let’s see what that means and why it’s a perfectly reasonable question to ask, given how we are taught about the electromagnetic spectrum. Maybe some of you will be so used to the usual electromagnetic wave representation, that you may not have stopped to think about it that much recently…
Above is a snapshot in time of an electromagnetic wave – a microwave, for example. The black arrow is the direction of travel of the microwave. The representation is one of a transverse wave (the disturbance is at right angles to the direction of motion). My friend knew that ‘microwaves are electromagnetic waves’ and that ‘electromagnetic waves are transverse’ – that’s part of what was misleading him!
In the case of an electromagnetic wave, what is the ‘disturbance’? The blue and yellow shapes in the diagram are oscillating electromagnetic fields – see their oscillatory shape along the length of the wave? In particular, as drawn on this page the electric field is shown in yellow, and the magnetic field is in blue. Two wavelengths’ worth of microwave are shown. The fields are mutually perpendicular – the electric field is in the horizontal plane, and the magnetic field is in the vertical (that’s not always true – I just happen to have drawn it like that). The two fields are also proportional to each other: where one is zero, so is the other; where one is a maximum, so is the other. They have the same sinusoidal shape.
Now, a tiny digression. In Magritte’s picture, The Treachery of Images – see half way down the page on the Los Angeles Count Museum of Art website – there is a picture of a pipe with the words “Ceci n’est pas une pipe” (this is not a pipe). The point is that it is a representation of a pipe, not the pipe itself. In the same way, the blue and yellow parts of the drawing above are not fields. They are representations of fields. And they are drawn in a way that can lead to the misconception we are discussing.
So let’s get to the heart of that misconception. First we’ll simplify the picture by getting rid of the electric field. We already know that the two fields act in synchrony, so this shouldn’t be too problematic. Here we go.
When we draw electromagnetic waves like this, it is easy to think that they have a top (crest) and bottom (trough). This train of thought can make us think the microwave represented above has a ‘height’ (and a width if we reinstate the yellow bit). That train of thought is reinforced by our picture of water waves, which are the exemplar for transverse waves.
https://pixabay.com/en/wave-ocean-sea-water-nature-blue-1905610/ under CC0 licence
This water wave is similarly travelling from left to right1. We can picture peaks and troughs on this wave, but in this case, the wave really does have a spatial extent in the vertical direction. The peaks are higher than the troughs. The amplitude of the wave is a real vertical displacement from the equilibrium water level.
So back to microwaves. If our representation of microwaves leads us to believe they have a height in space – they are transverse, after all – the question of whether they can fit through the holes in the microwave makes perfect sense.
So don’t they have a height?
Well, let’s change our representation of the microwave and see whether it alters how we ‘see’ it.
Firstly, we can ask, what even are those blue and yellow wiggly lines, if they aren’t actual places in 3-D space (such as is the case for the water wave)? And the answer is they are graphs of the strength of the electric and magnetic fields. Electric and magnetic fields are vectors, and the blue and yellow wiggles show the strength of the fields – the magnitudes and directions of those vectors – at points along the direction of travel (black arrow), not above and below it. We can show this more clearly by putting a few vector arrows on the drawing – they are arbitrarily spaced: there is an infinity of arrows we could have drawn corresponding to the infinity of points along the black arrow.
Let’s reiterate that point. Those arrows are not identifying points in space above and below the black line (as they might be with a water wave). They are assigning field strengths to points on the black line.
And because it’s easier to think about a few things than an infinity of things (probably), let’s remove the wiggly line, and leave the vector arrows.
So the arrows represent the strengths of the magnetic field at the designated points along the black line, and they have numerical values. Let’s imagine that the amplitude is 10 ‘magnetic field units’; then the vector arrows will have values between +10 and -10 (we just need to define which direction is positive – let’s say ‘up = positive’). Then the diagram above can have the values added to the arrows.
At this point we have a redundancy of information. The arrows and the numbers contain the same information, so we won’t lose anything if we retain the numbers and discard the arrows.
We only turned the arrow light blue so that we could superimpose the numbers on top – there is no further significance to the colour scheme, except to be a reminder that the values are magnetic field strength, and magnetic field was originally drawn in blue.
So this diagram is our end point. We have a new representation of electromagnetic waves, in which we attach a number to point along the wave.
And to answer the question in blue above: this representation does not hint that the wave has a vertical spatial extent. That was purely a result of the representing fields in a graphical form.
And it doesn’t resemble a photograph of a water wave either, so we are not tempted to import inappropriate similarities into this situation. Just to be clear I’m not claiming to have invented this representation; it’s just that the wiggly-blue-and-yellow picture is the one always seen in books, with no mention of the possible misconception it can bring.
If we no longer think the amplitude of the wave is linked to a spatial extent, then we won’t think it is a relevant consideration for the question of whether the microwave will fit through the hole! Remember, that question is still a good one – it just isn’t linked to the amplitude2. And, hopefully now, you have fewer reasons to think that it ever would be. I’m not saying that electromagnetic waves should never be drawn as the classic picture of a transverse wave, just that we need to look at that picture in a particular way to avoid misunderstanding it.
1 Before anyone says it is breaking and therefore isn’t technically a wave, I know, but the picture was pretty.
2 A well-known science website describes microwave ovens as follows: ‘You can see into the oven when the door’s shut because light can get through the holes in the gauze. Microwaves, however, are much bigger than light waves, so they’re too big to get through the holes and remain safely “locked” inside.’ You need a really clear idea about what ‘bigger’ means in order to interpret this clearly. What it really means is ‘of longer wavelength’, but it would be very easy to interpret it as ‘taller and wider’, as we have seen in this post.