Trigonometry

A laser beam excels as an industrial drill because it can be focused into a tiny bright point. Of course, ordinary light can be focused in a similar way. For instance, a magnifying glass held up to the sun will focus the sun's rays into a tiny, very bright point, a point that is also hot enough to burn a leaf or ignite a piece of paper.

Now consider collimated laser light, which is hundreds of times more directional than ordinary light. It can be focused to produce a beam of light, much hotter than the surface of the sun, that can cut cleanly through a thick metal bar in a few millionths of a second.

One of the more important uses of the laser drill in industry is in the production of copper wire. The wire is formed by forcing copper metal into a small round hole that a laser has drilled into a diamond. The hard diamond acts like a mold, and the much softer copper squeezes out the other end in the form of wire. The old method of drilling holes in industrial diamonds was very time-consuming and expensive. Since the only naturally occurring material hard enough to cut through a diamond is another diamond, workers had to use diamond drills. But diamonds are expensive. Furthermore, the drilling process took several hours, so a worker could drill only two or three holes in a workday. In contrast, a laser beam drills holes in diamonds at the speed of light. One worker using one laser can bore hundreds or even thousands of holes in a single hour. And the same method is used for drilling holes in other gems that are used as moving parts in watches.

These tiny diamond dies used in telephone lines have been drilled with laser beams. Such small holes could not be cut in diamonds without lasers.

Though it might seem surprising, lasers are also effective in boring holes in very soft materials. Some of these materials are easily stretched or torn by ordinary methods. An excellent example is the common baby bottle nipple. A laser beam burns a perfectly round hole in the top of the nipple without disturbing any of the surrounding rubber. Similarly, lasers are used to drill tiny holes in the soft plastic valves of spray cans (such as those of hair spray or glass cleaner). One such laser can punch over a thousand valve holes in one minute.

Another industrial application of lasers is welding. The advantage of the laser over normal welding methods is similar to its advantage in other industrial areas. The laser is hotter, faster, more accurate, and also safer because the welder does not have to go near the hot metal.

Laser welding works on both large and small scales. On the large scale, the U.S. Navy uses lasers to weld together huge metal parts in shipbuilding. Experts estimate that millions of dollars are saved in the welding process and millions more in reduced need for later repairs. Such common items as automobile spark plugs, portable batteries, and metal braces for the teeth are also routinely welded by laser beams.

On a smaller scale, lasers weld the parts for tiny electrical circuits used in computers, calculators, and miniature television sets. In the past, welding these small parts was accomplished by soldering---melting a metallic substance called solder around them to ensure a proper electrical connection. But soldering tools cannot be made small enough to weld the very tiny electrical parts now being produced; and manipulating the smallest available soldering tools is very painstaking work, produces uneven results, and can damage the delicate parts. By contrast, such tiny welds, some of them even microscopic, are easily made by the hot, razor-thin beam of a carbon dioxide laser.

In industry the opposite of welding is cutting, another essential process for making all manner of products.

A technician uses a laser to cut holes in carbon steel, one of the hardest of all artificial substances.

Every good toolbox has a hacksaw and a pair of scissors; the saw to cut metal, the scissors to cut cloth. The toolbox laser can do the jobs of both. Making saw blades themselves is an excellent example of using lasers to cut metal. The old methods of producing saw blades involved many steps, each of which required a person to handle the blades with his or her hands; not surprisingly, injuries were common. In contrast, a laser cuts the blade out of the sheet metal in only one step. Only the beam touches the metal, so as long as the operator is wearing protective glasses there is no chance for injury. In addition, reflective substances like glass can be cut by a laser if their surfaces are first coated with a dark substance. That way the laser light is absorbed rather than reflected.

An example of the use of "laser scissors" is to cut patterns for clothes. A laser cloth-cutting system was designed by Hughes Aircraft, the company that employed Theodore Maiman, the inventor of the ruby laser. The system works in the following way: Pieces of cloth are laid out on a large table while the patterns are entered into a computer, which decides the best way to trace them out on the cloth. Next, the computer directs the laser beam to cut out the traced patterns very precisely. Cloth for hundreds of suits can be cut in an hour, and as an added advantage the heat of the beam keeps the edges of the cloth from fraying.

Such laser scissors can be made to work on a microscopic level as well, not only in industry but also in biological research. Scientists who study and attempt to manipulate plant or animal cells can use a laser beam to make tiny alterations---in a sense performing microsurgery---on such cells. Recent experiments show that the use of lasers also can eliminate a serious obstacle to such microscopic manipulation; namely, the difficulty of holding a cell in place while working on it. To accomplish this task laser scissors are often accompanied by "laser tweezers," as explained by University of California scholar Michael Berns:

That light can heat or burn, measure or calibrate makes sense. But the idea of light creating a force that can hold and move an object may seem as fanciful as a Star Trek tractor beam. Still, light has momentum [a forward-pushing force] that can be imparted to a target. The resultant [very small] forces fall far below our sensory awareness when, for example, the sun's light falls on and imperceptibly pushes against us. But these forces can be large enough to influence biological processes at the subcellular level, where the masses of the objects are [extremely tiny]. . . . When the geometry of the arrangement of light beams and target is correct, the momentum imparted to the target pulls the target in the direction of the . . . laser beam, and the beam can thus hold the target in place. By moving the beam, the laser operator can pull the target from place to place. 2

The sine of 1 (rad) is 0.8414709848078965066525023216303.

The sine of an angle of 1 degree (from the computer's calculator) is 0.017452406 (correct to 9 decimal places).