ELA Component

Every day, Snell woke up in the morning, went to work at nine, and came back home at five- thirty. He took the same car every time. His work was built around punctuality. He never failed. Each morning, he made sure to get to work on time and eat a sufficient breakfast. There was a time when his health driven appetite’s fancy was not pleased by the quality of a doughnut, but, about four months ago, his friend Fermat mentioned how the “sugar within the doughnut would wake him up and keep his mind active. "Haven’t you noticed how complimentary a doughnut can to be to coffee?” he said. At this, Snell decided he would add the consumption of a doughnut to his daily routine. There was one concern though: The local doughnut bird of his work building only lay one doughnut each hour at about the half hour mark, so Snell would have to depart from his house at an earlier time in order to claim this doughnut at work before his co-workers did. “Well,” thought Snell, “It’ll be worth it. I can definitely leave the house ten minutes earlier and make it here to claim the doughnut before everyone else.” So that is exactly what he did for those past few months.

The road Snell took to work consisted of two parts: a regular paved road and the other a dirt road. Snell was able to travel faster on the former of course. Snell’s work building was ten miles northwest of his house. The paved part of the road, although still leading northwest, directed him more south than his destination was. Then, the unpaved part of the road went from the end of the paved and directed him straight to his destination. This was the road that Snell took even before he had decided he would make it to work early each morning to claim his prize. Snell was convinced, though, that this was not the fastest way to get there. For he persisted that if he could just take a road that went directly from his house to work, his travel time would be shortest. This tormented him for years, until finally his desire for a direct route was met with the new set of roads the city had just finished constructing. He was full of jubilation at this as he now figured he wouldn't have to wake up ten minutes earlier each morning. Oh, how Snell valued his sleep being that he often had to stay up late working on proposals. That very night, Lenny set his alarm to disrupt his dormancy at 8:10 am rather than the usual- 8 am. 8 am was the time he used to wake up at before it was necessary to get to work early for the doughnut. How great the thought was to him to wake up at the same time as before and still get his morning treat.

The next morning, he woke up as his alarm directed him to, showered, brushed his teeth, and peed (all at the same time), ironed his shirt, and listened to music as he put on his attire. This day, he was wearing gray slacks and a light brown jacket with elbow pads. Once he was ready, he stepped into his car and begun the ride he had now looked forward to for the first time in years.

He got to work, ignorant enough to check his time of arrival for he knew he was right. Yet, as he walked into the building, he noticed no ring on the nest of the doughnut bird. He squinted his eyes and scrutinized the nest the best he could from the far distance he was from the nest. His heart was suddenly met with a cold hand. He was not accepting though, so he ran to the nest where he would brush his hand around frantically to make sure there really was no doughnut; there wasn’t. Without thinking, he turned his head enough to meet his eyes with the digital clock that was mounted near the door of the cafe. “9:00,” the clock displayed. He was too late. Snell then took the thought that he was wrong and buried it at the bottom of a boiling pot. He did not want to accept his mistake. Throughout the day, he worked stringently, forgetting about his erroneous action of that morning by the lid he held tightly on the boiling pot which was shaking violently. After he finished his work though, and took the same road he used that morning, the lid to the pot was becoming more and more furious, trying to shake its way off. The road reminded him of his mistake so much that now the lid made its success in flying off and Snell felt it. Try again he decided would be his plan. Maybe some other variable led to his being late that morning. So he did the very next morning. When he got to work the next day though, the doughnut was again not there and the clock still displayed “9:00.” Infuriated even more he was. This time, so livid that he could not even begin to keep the lid on the pot. He worked less stringently, not only because of his frustration, but also because he did not have his daily doughnut for the second time that morning. Gosh, how he resented the occurrence of that morning

On his way back home though, it hit him. He realized that the fastest way to work was not particularly to the shortest way. He realized that since he traveled slower on the dirt road, he needed to minimize the distance traveled on this part of the road as much as possible- maximizing his distance traveled on paved road. Although overall distance would not be shorter, he figured, travel time would.

This night, as he was ever more confident of his idea, he kept the alarm set to wake him at 8:10 am as it had the two preceding mornings. The next morning, he followed his normal list of actions and made his way to work on the road that met his newly formulated route. This was a road that had existed long before the two others. He was mad at himself for never realizing that this road, which originally seemed like an anachronism, was indeed the solution to his dilemma. All was great until Snell could not believe the retina of his eye as he walked into his work building. The doughnut was still.not.there. At this point, he decided he wouldn’t even try it again the next morning. He was infuriated, livid, upset, and could be described by any other word that represented complete anger. His face was as red as the whitest politician in America. His armpits emitted excessive beads of sweat that ran down the sides of his torso. It was at this moment he decided he would never face the issue again. He put a lock on the lid of the boiling pot that had taunted him before; a lock that would not be open for quite some time. Snell was to resort back to his waking up at 8 am and taking the original route of his trip to work to get his doughnut. He was still convinced, though, that this was not the shortest route.

The three roads that Snell uses in attempting to find the fastest way to work. The middle one, of course, is the fastest route. While this is not in any way up to scale, it is meant only to introduce one to the concept of Snell's law and Fermat's principle of least time. Refer to the image below for a brief explanation and how Snell's story connects to the story of how light finds the fastest route to take according to Fermat's principle of least time.

Note: this image also is not drawn to scale. For a scaled image with mathematical explanation, visit "Snell's Law" Page (soon to come).

If asked to choose the fastest path from point A to point B, there are two most common answers: one that follows the red path and the other that follows the blue path. The justification behind the red paths being the fastest is that the distance traveled through the faster medium is maximized and the distance through the slower minimized. The overall distance of this path is so substantially long ,though, that it makes the minimization of distance in the slower medium irrelevant. For the blue path, the justification is , of course, that it is the shortest distance there. Although it is, in fact, the net shortest distance, it is not the fastest due to its having the most distance in the slower medium and the least distance in the faster. The red and blue paths are actually the slowest paths. The fastest is a perfect balance between the two. A path that optimizes best the shortest net distance factor and the minimization of distance through slower medium factor. This "perfect balance" of a route is only capable of being found using rather complex mathematics. Amazingly though, light, will always refract, and (without using complex mathematics) follow the "perfect balanced" route no matter what the situation is.