No, there is no square-peg in round-hole effect going on in microwave ovens. Microwaves reflect from conducting surfaces, just as light waves reflect from shiny metals, and they can't pass through holes in conducting surfaces if those holes are substantially smaller than their wavelengths. The holes in the conducting mesh covering the microwave oven's window are simply too small for the microwaves and the microwaves are reflected by that mesh.
Microwaves themselves have no well-defined shape but they do have firm rules governing their overall structures. Books usually draw microwaves (and all other electromagnetic waves) as wavy lines, as though something was truly going up and down in space. From that misleading representation, it's easy for people to suppose that electromagnetic waves can't get through certain openings.
In reality, electromagnetic waves consist of electric and magnetic fields (influences that push on electric charge and magnetic pole, respectively) that point up and down in a rippling fashion, but nothing actually travels up and down per say. The spatial structures of these fields are governed by Maxwell's equations, a set of four famous relationships that bind electricity and magnetism into a single, unified classical theory. Maxwell's equations dictate the structures of electromagnetic waves and predict that electromagnetic waves on one side of a conducting surface can't propagate through to the other side of that surface. Even if there are small holes in the conducting surface, holes that are much smaller that the wavelength of the waves, those waves can't propagate through the surface. More specifically, the fields die off exponentially as they try to penetrate through the holes and the waves don't propagate on the far side.
The choice of round holes in the oven mesh is simply a practical one. You can pack round holes pretty tightly in a surface while leaving their conducting boundaries relatively robust. And round holes treat all electromagnetic waves equally because they have no wide or narrow directions.
Yes, but it's not a good idea. Depending on the type of plate, you can either damage your microwave oven or damage the plate.
If a plate is "microwave safe," it will barely absorb the microwaves and heat extremely slowly. In effect, the microwave oven will be operating empty and the electromagnetic fields inside it will build up to extremely high levels. Since the walls of the oven are mirrorlike and the plate is almost perfectly transparent to microwaves, the electromagnetic waves streaming out of the oven's magnetron tube bounce around endlessly inside the oven's cooking chamber. The resulting intense fields can produce various types of electric breakdown along the walls of the cooking chamber and thereby damage the surface with burns or arcs. Furthermore, the intense microwaves in the cooking chamber will reflect back into the magnetron and can upset its internal oscillations so that it doesn't function properly. Although magnetrons are astonishingly robust and long-lived, they don't appreciate having to reabsorb their own emitted microwaves. In short, your plates will heat up slowly and you'll be aging your microwave oven in the process. You could wet the plates before putting them in the microwave oven to speed the heating and decrease the wear-and-tear on the magnetron, but then you'd have to dry the plates before use.
If a plate isn't "microwave safe," then it will absorb microwaves and heat relatively quickly. If it absorbs the microwaves uniformly and well, then you can probably warm it to the desired temperature without any problems as long as you know exactly how many seconds it takes and adjust for the total number of plates you're warming. If you heat a plate too long, bad things will happen. It may only amount to burning your fingers, but some plates can't take high temperatures without melting, cracking, or popping. Unglazed ceramics that have soaked up lots of water will heat rapidly because water absorbs microwaves strongly. Water trapped in pores in such ceramics can transform into high-pressure steam, a result that doesn't seem safe to me. And if a plate absorbs microwaves nonuniformly, then you'll get hotspots or burned spots on the plate. Metalized decorations on a plate will simply burn up and blacken the plate. Cracks that contain water will overheat and the resulting thermal stresses will extend the cracks further. So this type of heating can be stressful to the plates.
That tear in the window screen presents three potential problems: microwave leakage, evanescent waves, and arcing. As long as the hole is small, less than a centimeter or so, it's not likely to allow much microwave leakage. The oven's microwaves have a wavelength of 12.4 centimeters and they'll reflect from conducting surfaces with holes much smaller than that wavelength. A foot from your oven, there probably won't be any significant microwave intensity, although the only way to be sure is with a microwave leakage meter.
The evanescent wave problem is more likely. When any electromagnetic wave reflects from a conducting surface that has small holes in it, there is what is known as an evanescent wave extending into and somewhat beyond each hole. It's as though the wave is trying to figure out whether or not it can pass through the opening and so it tries. Even when it discovers that the hole is far too small for it pass through (i.e., much smaller than its wavelength), it still offers electromagnetic intensity in the region just beyond the hole. The extent of the evanescent wave increases with the size of the hole. The microwave oven's screen has very small holes and it is located inside the glass window. The evanescent waves associated with those holes cut off so quickly that you can hold your hand against the glass and not expose your skin to significant microwaves. But once you've torn a larger hole in the screen, the evanescent waves can extend farther through that screen and perhaps out beyond the surface of the glass window. If you press your hand against the window just in front of the tear while the microwave oven is on, you may burn your hand.
Finally, there is the issue of arcing. To reflect the microwaves, the conducting screen must carry electric currents. The microwaves' electric fields push electric charge back and forth in the conducting screen and it is that moving charge (i.e., electric current) that ultimately redirects the microwaves back into the cooking chamber as a reflection. Those electric currents in the screen are real and they're not going to take kindly to that tear. It's a weak spot in the conducting surface through which they flow. Weak electrical paths can heat up like lightbulb filaments when they carry currents. Moreover, charge that should flow across the torn region can accumulate on sharp edges and leap through the air as an arc. If either of these processes happens, it may scorch the window and the screen, and cause increasing trouble.
You could be lucky: the leakage could be zero, the evanescent waves could remain far enough inside the window to never cause injury, and the tear could never heat up or arc. But the risk of operating this damaged microwave oven is not insignificant. Since it's an installed unit, I'd suggest replacing the screen or the door. There are a number of websites that sell replacement parts for microwave ovens and I have used them to replace the door on our microwave oven.
You're right. Whether the microwave oven is grounded or not makes no difference on its screen's ability to prevent microwave leakage. In fact, the whole idea of grounding something is nearly meaningless at such high frequencies. Since electrical influences can't travel faster than the speed of light and light only travels 12.4 cm during one cycle of the oven's microwaves, the oven can't tell if it's grounded at microwave frequencies; its power cord is just too long and there just isn't time for charge to flow all the way through that cord during a microwave cycle.
When you ground an appliance, you're are making it possible for electric charge to equilibrate between that appliance and the earth. The earth is approximately neutral, so a grounded appliance can't retain large amounts of either positive or negative charge. That's a nice safety feature because it means that you won't get a shock when you touch the appliance, even if one of its power wires comes loose and touches the case. Any charge that the power wire tries to deposit on the case will quickly flow to the earth as the appliance and earth equilibrate.
But charge can't escape from the appliance through the grounding wire instantly. Light takes about 1 nanosecond to travel 1 foot and electricity takes a little longer than that. For charge to leave your appliance for the earth might well require 50 nanoseconds or more. That's not a problem for ordinary power distribution, so grounding is generally a great idea. Each cycle of the 60-Hz AC power in the U.S. takes 18 milliseconds to complete, so the appliance and earth have plenty of time to equilibrate with one another. But a cycle of the microwave power in the oven takes less about 0.4 nanoseconds to complete and there's just no time for the appliance and earth to equilibrate. At microwave frequencies, the electric current flowing through a long wire is wavelike, meaning that at one instant in time the wire has both positive and negative patches, spaced half a wavelength apart along its length. It's carrying an electromagnetic ripple.
The metal screen on the oven's door has to reflect the microwaves all by itself. It does this without a problem because the holes are so much smaller than 12.4 centimeters that currents easily flow around them during a cycle of the microwaves. Those currents are able to compensate for the holes in the screens and cause the microwaves to reflect perfectly.
I figure that some day, we'll turn to our landfills as resources for precious elements like copper and gold. That assumes, of course, that we survive global warming. In the meantime, we'll just keep throwing stuff out.
Despite the scary title "microwave radiation," a microwave oven is basically just another household electronic device. It is an extremely close relative of a convention cathode-ray-tube television set. If you're OK with putting CRT televisions and computer monitors in the landfill, you should have no problems with putting microwave ovens there, too. Even when the microwave oven is on, all it has inside it is microwave radiation and that's just not a big deal. The instant you turn it off, it doesn't even have those microwaves in it. It's just boring inert electronic parts and they'll sit in the landfill for generations, rusting and decaying like every other abandoned electronic gadget. I'd rather see it go to a recycling center and have its precious materials returned to the resource bin, but as landfill junk goes, it's not all that bad. Given that toxic chemicals are the primary concern with landfills, microwave ovens are probably rather innocuous. They have no radioactive contents and although the high-voltage capacitor might have oil in it, that oil can no longer be the toxic PCBs that were common a few decades ago. Even when that oil leaks into the environment, it's probably not going to do much.
So there you have it, microwave ovens go to their graves no more loudly or dangerously than old televisions or computers or cell phones.
In fact, I might start calling cell phones "microwave phones" because that's exactly what they are. They communicate with the base unit by way of microwave radiation. Given the number of people who have cell phones semi-permanently installed in their ears, concerns about microwave radiation should probably be redirect from microwave ovens to "microwave phones." Think about it next time your six-year-old talks for an hour with her best friend on that "microwave phone."
What you propose to do is far more difficult than you imagine. Determining the chemical contents of food is hard, even with a well-equipped laboratory and permission to destroy the food in order to study it. The idea of analyzing a casserole in detail simply by beaming microwaves at it is science fiction. Think how much easier airport security would be if they could chemically analyze everything that came in the front door just by beaming microwaves at it.
That said, however, let me make two comments. First, the question quickly turns to computer interface issues, as though the chemical analysis part is trivial in comparison to computer presentation part. Physical science and computer science are truly different fields and not everything in the scientific domain can be reduced to a software package. Physics and chemistry haven't disappeared with the advent of computers and there will never be a firmware upgrade for your microwave oven that will turn it into a nutritional analysis laboratory. As a society, we've gone a bit too far in replacing science education with technology education, particularly computer software.
Second, while remote chemical analysis isn't easy, it can be done in certain cases with the clever use of physics and chemistry. One of my friends here at Virginia, Gaby Laufer, has developed an instrument that studies the infrared light transmitted by the air and can determine whether that air contains any of a broad variety of toxic or dangerous gases in a matter of seconds. Air's relative transparency makes it easier to analyze than an opaque casserole, but even when you can see through something it's not trivial to see what it contains. Gaby's instrument does a phenomenal job of fingerprinting the gas's absorption features and identifying trouble.
Note added: a reader informed me that there are now microwave ovens that can read bar codes and adjust their cooking to match the associated food. A scale in the base of the oven can determine the food's weight and cook it properly. Another reader suggested that a microwave oven might be able to measure the food's microwave absorption and weight in order to adjust cooking power and time. While that's also a good possibility, ovens that sense food temperature or the humidity inside the oven can achieve roughly the same result by turning themselves off at the appropriate time.
I think that you've rediscovered an experiment in which people cut a grape almost in half, open the two halves like a book and lay it flat on a plate. In the microwave, the thin bridge between the halves carbonizes and than emits flames. Basically, the fruit pieces or berries are acting as antennas for the microwaves, which drive electric currents through the narrow bridges between parts. The berries aren't great conductors, but they're not true insulators either. Those bridges overheat (like an overloaded extension cord) and burn up. The flames come from the burning bridges.
If you let the flames go on long enough and enough carbon develops, you'll probably start getting plasma balls in the oven (lots of fun, but not great for the oven... you can scorch its top surface because those plasma balls rise and skittle around the ceiling of the oven). Anyway, you can probably find the carbon areas if you look closely enough, but they're no worse than a little burnt toast.
Most likely, the ant never left the floor or walls of the microwave oven, where it was as close as possible to those metal surfaces. The six sides of the cooking chamber in a microwave oven are made from metal (or painted metal) because metal reflects microwaves and keeps them bouncing around inside the chamber.
Metals are good conductors of electricity and effectively "short out" any electric fields that are parallel to their surfaces. Microwaves reflect from the metal walls because those walls force the electric fields of the microwaves to cancel parallel to their surfaces and that necessitates a reflected wave to cancel the incident wave. Because of that cancellation at the conducting surfaces, the intensity of the microwaves at the walls is zero or very close to zero.
The ant survived by staying within a tiny fraction of the microwave wavelength (about 12.4 cm) of the metal surfaces, where there is almost zero microwave intensity. Had the ant ventured out onto your cup, it would have walked into real trouble. Once exposed to the full intensity of the microwaves, it would not have fared so well.
It's quite possible that the pattern of microwaves inside your oven is more intense at some places than in others — that's why most microwaves have carousels in them to move the food around. I don't think that the pattern will change much with age, but it's possible that your oven isn't producing as much microwave power as it once did and you notice the low-intensity regions more than before. It's not a true "fault", but it is a nuisance. If you get tired of putting up with it, you should probably replace the oven. It used to be that you could purchase carousel inserts for the ovens, but I don't see them for sale anymore.
No, those gases don't absorb microwaves significantly regardless of frequency. Diatomic molecules are nearly oblivious to long wavelength electromagnetic waves. In fact, that's why they don't contribute to the "greenhouse effect." Oxygen does have an unusual absorption band in the near infrared, but that's about it.
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