SVYASHCHENNYE! (SACRED)

"The frontiers of the Soviet Union are sacred!" thundered Andrey Gromyko in September 1983, excusing the cut-throats who had just shot down an airliner with 269 passengers on board.

But the Sacred Goddess was defiled by a 19-year-old German who flew his Cessna all the way to Moscow and landed it in Red Square, two days after the Soviet Border Guard Day. After another two days, the Soviet Defense Minister was retired and the com-mander of Soviet air defenses sacked, which filled my charitable heart with double glee: first, because they were disgraced, and second, because they were disgraced, at least in part, innocently. There are certain reasons that make defense against irrational acts difficult; and low flying aircraft, once they have passed the border defenses, cannot be detected by distant, ground-based radars.

Both are scientific points, and we shall take a closer look at them.

The reason why ground-based radars cannot detect low objects at a distance (but still above the horizon) has to do with reflection at very small angles of elevation. When a propagating wave (no mat-ter whether sound, light, or a wave on the water) hits a plane inter-face in a direction making a very small angle with the plane, all of its energy is reflected, even though at steeper angles some or all of it might penetrate into the medium beyond the interface.

To take an analogy with objects more familiar than waves, a stone thrown onto the surface of water sinks. But if you are male and older than 10, you also know that a flat stone thrown onto the surface at a very small angle will be "reflected," that is, will be bounced off the surface; if you were very good, you could make it bounce 3 or 4 times in succession.

For wave motion, in particular for light, the complete laws of reflection were discovered by one of the great geniuses of science, Augustin Jean Fresnel (pron.freNEL, 1788-1827), originally a civil engineer working on France's roads and bridges, who adhered to the royalist cause during the "Hundred Days" (Napoleon's rule bet-ween his escape from Elba and the Battle of Waterloo, both in 1815), and was therefore suspended.

Fresnel was a brilliant mathematician, and among his numerous discoveries were the laws of reflection of light (and, as we know to-day, of all electromagnetic radiation) at the plane boundary of two media, such as air and glass: how much penetrates into the other medium, and how much is reflected back into the first. This depends not only on the optical properties of the two media, but also on the angle of incidence; and the very general Fresnel formula for reflection shows that when the angle of elevation is very small, then all of the incident wave gets reflected, regardless of the optical properties of the two different media adjoining the plane boundary. At "grazing incidence" (as opticians, acousticians and elec-tromagneticists call this case of small elevation angles) everything gets reflected.

Why? Look at it this way: If you try to break down a door, you may or may not succeed if you ram it with your shoulder at right angles to the plane of the door; but you will hardly succeed if you try to ram it at a very small angle, and if you make that angle zero (moving parallel to the door, brushing it with your shoulder), you won't break it down even if it is made of paper. Neither can a wave get into the other medium if it propagates at a very small "grazing angle"(ACD below); but if none can get in, then the conservation of energy requires that all stay out, so that all of the wave gets reflected.