radiation takes it! with a narrow slit, more radiation reaches D' than reaches it with a wide slit One can do the same thing with light, but it is hard to demonstrate on a large scale. The effect can be seen under the following simple conditions. Find a small bright light, say an unfrosted bulb in a street light far away or the reflection of the sun in a curved automobile bumper. Then put two fingers in front of one eye, so as to look through the crack, and squeeze the light to zero very gently. You will ee that the image of the light, which was a little dot before, becomes quite elon- gated, and even stretches into a long line. The reason is that the fingers are very close together, and the light which is supposed to come in a straight line is spread out at an angle, so that when it comes into the eye it comes in from several direc- tions. Also you will notice, if you are very careful, side maxima, a lot of fringes along the edges too, Furthermore, the whole thing is colored. All of this will be explained in due time, but for the present it is a demonstration that light does not always go in straight lines, and it is one that is very easily performed 26-6 How it works Finally, we give a very crude view of what actually happens, how the whole thing really works, from what we now believe is the correct, quantum-dynamically accurate viewpoint, but of course only qualitatively described. In following the light from A to B in Fig. 26-3, we find that the light does not seem to be in the form of waves at alL. Instead the rays seem to be made up of photons, and they lighr produce clicks in a photon counter, if we are using one. The brightness of proportional to the average number of photons that come in per second and what we calculate is the chance that a photon gets from A to B, say by hitting the mirror. The law for that chance is the following very strange one. Take any path and find the time for that path; then make a complex number, or draw a little complex vector, pe, whose angle e is proportional to the time. The number of turns per second is the frequency of the light. Now take another path; it has, for Istance, a different time, so the vector for it is turned through a different angle- he angle being always proportional to the time. Take all the available paths and dd on a little vector for each one; then the answer is that the chance of arrival of the photon is proportional to the square of the length of the final vector, from the beginning to the end Now let us show how this implies the principle of least time for a mirror. We consider all rays, all possible paths ADB, AEB, ACB, etc, in Fig. 26-3. The path A DB makes a certain small contribution, but the next path, AEB, takes a quite different time, so its angle e is quite different. Let us say that point Corresponds to minimum time, where if we change the paths the times do not change. So for awhile the times do change, and then they begin to change less and less as we get near point Fig. 26-14. The summation of proba C( Fig. 26-14). So the arrows which we have to add are coming almost exactly at bility amplitudes for many neighboring the same angle for awhile near C, and then gradually the time begins to increase again, and the phases go around the other way, and so on. Eventually, we have quite a tight knot. The total probability is the distance from one end to the other squared. Almost all of that accumulated probability occurs in the region where all the arrows are in the same direction(or in the same phase). All the contributions fre the paths which have very different times as we change the path, cancel them- selves out by pointing in different directions. That is why, if we hide the extreme parts of the mirror, it still reflects almost exactly the same, because all we did was to take out a piece of the diagram inside the spiral ends, and that makes only a very small change in the light. So this is the relationship between the ultimate picture of photons with a probability of arrival depending on an accumulation of arrows. an nd the principle of least time