only one part in eight million of the radius, the cusps of the hypocycloid are enormously sharp compared with the distance between them. The acceleration which involves a second derivative with respect to time, gets twice the"compression factor" 8x 10 because the time scale is reduced by eight million twice in the neighborhood of the cusp. Thus we might expect the effective wavelength to be much shorter, to the extent of 64 times 102 smaller than 20 meters, and that corresponds to the x-ray region. (Actually, the cusp itself is not the entire determining factor; one must also include a certain region about the cusp thi changes the factor to the 3/2 power instead of the square, but still leaves us above the optical region. )Thus, even though a slowly moving electron would have radiated 20-meter radiowaves, the relativistic effect cuts down the wavelength so 2- much that we can see it! Clearly, the light should be polarized, with the electric Pulse from electron field perpendicular to the uniform magnetic field sug. To further appreciate what we would observe, suppose that we were to take th light (to simpli because these pulses are so fa rt in time shall just take one pulse)and direct it onto a diffraction grating, which is a lot of scattering wires. After this pulse comes away from the grating, what do we see (We should see red light, blue light, and so on, if we see any light at all. )what do we see? The pulse strikes the grating head-on, and all the oscillators in the grating, together, are violently moved up and then back down aga5.But the They then produce effects in various directions, as shown in Fig point P is closer to one end of the grating than to the other, so at this point the ig. 34-5. The light which strikes a electric field arrives first from wire A, next from B, and so on; finally, the pulse grating as a single, sharp pulse is scat from the last wire arrives. In short, the sum of the reflections from all the succes tered in various directions as different wires is as shown in Fig. 34-6(a); it is an electric field which is a series of pulses and it is very like a sine wave whose wavelength is the distance between the pulses just as it would be for monochromatic light striking he ting! So, we get colored light all right. But, by the same argument, will we not get light from any kind of a pulse"?No. Suppose that the curve were much smoother; then we would add all the scattered waves together, separated by a small time between them(Fig 34-66). Then we see that the field would not shake at all, it would be a very smooth because each pulse does not vary much in the time interval between pulse The electromagnetic radiation emitted by relativistic charged particles cir- ulating in a magnetic field is called synchrotron radiation. It is so named for obvi- Fig. 34-6. The total electric field due ous reasons, but it is not limited specifically to synchrotrons, or even to earthbound to a series of (a) sharp pulses and (b) laboratories. It is exciting and interesting that it also occurs in nature