## How can you make a laser beam fade with distance?

#### Is it possible to make a visible laser beam fade after 2 or 3 feet for safety reasons? — RB, Arvada, Colorado

Since light carries energy, a laser beam can’t simply disappear after a couple of feet — something would have to absorb it and its energy. Since the atmosphere is extremely transparent to visible light, it won’t do the trick.

Since eye safety requires limiting the amount of laser power that can enter a person’s eye, you can make a laser more eye-safe by enlarging its beam. Even a powerful laser can be eye-safe if only a small fraction of the laser light can enter a person’s iris and focus on their retina.

Although it’s natural to think of a laser beam as a narrow pencil of light that stays narrow forever, that’s not really the case. The diameter of a laser beam changes with distance from its source. The beams from typical lasers, including laser pointers, start relatively narrow and widen as gradually as the physics of light propagation will allow. But with the help lenses, you can change that widening process dramatically. For example, if you send a typical laser beam through a converging lens that has a focal length of 1 foot, the laser beam will converge to a very narrow “beam waist” 1 foot beyond the lens and will then spread relatively quickly with distance. It will return to its original diameter 1 foot beyond its waist and to 10 times its original diameter 10 feet beyond its waist. With its light spread out by a factor of 10 in both height and width, it will have only 1/100th the intensity (power per unit area) of the original beam. Because of its large size, only a fraction of the beam and its light power will now enter a person’s iris and focus on their retina.

Using this scheme, you can have a beam that is extremely intense for the first 2 feet, including a super-intense waist at the 1-foot mark. But beyond that point, the beam spreads quickly and soon becomes so wide that it is no longer a eye hazard.

## Why do scantron-type tests only read #2 pencils? Can other pencils work?

#### Why do scantron-type tests only read #2 pencils? Can other pencils work? — MW, Montgomery, AL

The #2-pencil requirement is mostly historical. Because modern scantron systems can use all the sophistication of image sensors and computer image analysis, they can recognize marks made with a variety of materials and they can even pick out the strongest of several marks. If they choose to ignore marks made with materials other than pencil, it’s because they’re trying to be certain that they’re recognizing only marks made intentionally by the user. Basically, these systems can “see” most of the details that you can see with your eyes and they judge the markings almost as well as a human would.

The first scantron systems, however, were far less capable. They read the pencil marks by shining light through the paper and into Lucite light guides that conveyed the transmitted light to phototubes. Whenever something blocked the light, the scantron system recorded a mark. The marks therefore had to be opaque in the range of light wavelengths that the phototubes sensed, which is mostly blue. Pencil marks were the obvious choice because the graphite in pencil lead is highly opaque across the visible light spectrum. Graphite molecules are tiny carbon sheets that are electrically conducting along the sheets. When you write on paper with a pencil, you deposit these tiny conducting sheets in layers onto the paper and the paper develops a black sheen. It’s shiny because the conducting graphite reflects some of the light waves from its surface and it’s black because it absorbs whatever light waves do manage to enter it.

A thick layer of graphite on paper is not only shiny black to reflected light, it’s also opaque to transmitted light. That’s just what the early scantron systems needed. Blue inks don’t absorb blue light (that’s why they appear blue!), so those early scantron systems couldn’t sense the presence of marks made with blue ink. Even black inks weren’t necessarily opaque enough in the visible for the scantron system to be confident that it “saw” a mark.

In contrast, modern scantron systems used reflected light to “see” marks, a change that allows scantron forms to be double-sided. They generally do recognize marks made with black ink or black toner from copiers and laser printers. I’ve pre-printed scantron forms with a laser printer and it works beautifully. But modern scantron systems ignore marks made in the color of the scantron form itself so as not to confuse imperfections in the form with marks by the user. For example, a blue scantron form marked with blue ink probably won’t be read properly by a scantron system.

As for why only #2 pencils, that’s a mechanical issue. Harder pencil leads generally don’t produce opaque marks unless you press very hard. Since the early scantron machines needed opacity, they missed too many marks made with #3 or #4 pencils. And softer pencils tend to smudge. A scantron sheet filled out using a #1 pencil on a hot, humid day under stressful circumstances will be covered with spurious blotches and the early scantron machines confused those extra blotches with real marks.

Modern scantron machines can easily recognize the faint marks made by #3 or #4 pencils and they can usually tell a deliberate mark from a #1 pencil smudge or even an imperfectly erased mark. They can also detect black ink and, when appropriate, blue ink. So the days of “be sure to use a #2 pencil” are pretty much over. The instruction lingers on nonetheless.

One final note: I had long suspected that the first scanning systems were electrical rather than optical, but I couldn’t locate references. To my delight, Martin Brown informed me that there were scanning systems that identified pencil marks by looking for their electrical conductivity. Electrical feelers at each end of the markable area made contact with that area and could detect pencil via its ability to conduct electric current. To ensure enough conductivity, those forms had to be filled out with special pencils having high conductivity leads. Mr. Brown has such an IBM Electrographic pencil in his collection. This electrographic and mark sense technology was apparently developed in the 1930s and was in wide use through the 1960s.