One of the questions on everyone's lips at the moment is "How does a large passenger jet simply disappear from radar without trace?" It is clearly very distressing for anyone with friends or relatives on board – not knowing what has happened. As I write this, there still seems to be a complete lack of clear evidence pointing one way or another. I'm not an aviation expert so I really can't add anything of value here. But I can turn the question around to one of more physics relevance, which is "What allows a plane to be detected with radar in the first place?"
Radar, in concept at least, is pretty simple physics. It's name comes from an acronym "RAdio Detection AND Ranging". However, it has out-grown its acronym, since it now does more than simply detect and 'range' (tell the distance to), and 'radar' is now a word in itself and not spelled in uppercase. The basic idea is that a radio wave will reflect off a metal object (a plane, ship, your car…) and some of that wave will return to where it came from. To be pedantic, while we often think about the radio transmitter and detector being in the same place, this doesn't need to be the case. In fact the first radar systems had detectors physically separate from the receivers. Anyway, we know the speed at which radio waves travel (pretty well the speed of light in air) and therefore by timing the delay between transmitting and receiving we know how far the object is away. By also knowing the direction the reflections come from, we can therefore work out a position.
It gets a bit more difficult in practice, since radio waves don't necessarily travel in straight lines, but can be bent due to atmospheric conditions. And radar can tell us more than just position. For example, we can exploit the doppler effect to measure the how fast an object is travelling. Waves reflecting from a moving object return with a different wavelength – measure the wavelength shift and you measure how quickly the object is moving towards or away from you.
So why does a metal object reflect radio waves? That's down to its high electrical conductivity ensuring that there must be no electric field at the surface. The waves simply can't get into the material and are completely reflected. I won't bore you with the analysis of Maxwell's equations to show this – unless you happen to be in my third year electromagnetic waves class in which case I'll bore you with it – whoops, make that excite you with it – in a week's time. Metal makes a pretty good shield for radio.
Just what fraction of the power of the incident wave that gets reflected back towards the transmitter can be tricky to calculate. It's encapsulated in a term known as the 'radar cross section' (RCS). The definition of RCS is a little tricky to wrap one's head around, but I'll give you it: The radar cross section of an object, in a given direction and a particular frequency, is the cross sectional area of a perfectly-reflecting sphere that would give the same power return as the object gives in that direction. In other words, imagine a large, metal sphere, that reflects the same amount of power that our plane does. Take the cross-sectional area of it (pi times the radius squared) and that's the RCS. A large RCS means a large amount of power returned.
To some extent the RCS simply depends on how big an object is, but just as important is the shape of an object. Geometry with right-angles in it will cause large reflections back in the direction of the transmitter (think of a snooker table – if a ball bounces off two cushions it's direction of travel is reversed – it doesn't matter about the angle of incidence). Long edges also give large returns – they can act rather like antennas and re-radiate the incoming radiation. Unless you specifically set out to design an aircraft with a low RCS the chances are that what you'll end up with is something which has a pretty substantial RCS. The tail is at right-angles to the fuselage, it has long straight wings, and is made from highly reflective metal.
And that means that a Boeing 777 isn't likely to vanish off a radar screen while it remains in one piece.