The Physics of a Rainbow
by Courtney Sant

So some of you might be wondering, what exactly is a rainbow? We all enjoy spotting one in the sky on those rare occasions but few of us know why it got there in the first place. A rainbow can be described as a charming chromatic dispersion. It is formed when white sunlight is intercepted by a drop of water in the atmosphere and some of the light refracts into the drop, reflects from the drop's inner surface, and then refracts out of the drop. The first refraction separates the sunlight into its component colors and the second refraction increases the separation ultimately resulting as a rainbow. Colors of a rainbow are caused by the refraction and internal reflection of light rays that enter the raindrops. The concentration of rays near the minimum deviation gives rise to the arc of the rainbow. The incoming ray is unpolarized, and can be represented by two polarized waves whose planes of polarization are perpendicular to each other. There a few things that can happen to the ray when entering atmosphere. Part of the incoming ray is reflected back to the atmosphere; part of the light refracts into the drop and then refracts back to the atmosphere; some reflect from the drop’s inner surface and refract back to the atmosphere. Ultimately this refraction of rays give rise to an ordinary rainbow. In some cases, some rays will reflect twice inside the drop and then refract back to the atmosphere which ultimately gives rise to a secondary rainbow.

Rainbows briefly can be described as an optical and meteorological phenomena which cause a spectrum of light to appear in the sky when the sun shines onto droplets of moisture in the Earth’s atmosphere. As a result one can see a multicolored arc with red on the outside and violet on the inner arc. In most cases the spectrum of colors usually result in a sequence of Newton’s sevenfold red, orange, yellow, green, blue, indigo, violet or also known as Roy G. Biv.A secondary rainbow can be seen on rare occasions outside the primary arc with colors in the opposite order. Though rainbows are usually bow-shaped, there are also phenomena of rainbow-colored strips in the sky: in the shape of stripes, circles or even flames.

The rainbow is actually a disk of scattered light, but it is brightest at the edge; the disk for different wavelengths is a different size, and that is why we see the color effects there. When light refracts, it follows the law of refraction ni sin(ctai)=nr sin( ctar) where n is the index of refraction. There is an angle of incidence and an angle of refraction. Most of the light is refracted out by one ray. When your eyes intercept the separated colors from the raindrops the red color you experience is the product of when drops are angled slightly higher in the sky than when you experience seeing blue. Descartes and Willebrord Snell had determined how a ray of light is bent, or refracted, as it traverses regions of different densities, such as air and water. When the light paths through a raindrop are traced for red and blue light, one finds that the angle of deviation is different for the two colors because blue light is bent or refracted more than is the red light.

The overall effect is that the incoming light is reflected back over a wide range of angles with the most intense light at an angle of 40-42 degrees. The angle is independent of the size of the drop but does depend on its refractive index. For instance, seawater has a higher refractive index than rain water therefore the radius of a rainbow in the sea spray is smaller than an actual rainbow. It becomes visible to the eye due to a misalignment of these bows.

There are other variances of rainbows as well such as a reflection rainbow and fire rainbow. A reflected rainbow occurs when sunlight reflects off a body of water before reaching the raindrops. This particular rainbow shares the same endpoints as a regular rainbow however it has a far more greater arc when visible. In addition, both primary and secondary reflection rainbows can be seen. The reflected rainbow is not a mirror image of the primary bow but is displaced from it to a degree depending on sun’s altitude. The fire rainbow, also known as the circumhorizontal acr, is produced when sunlight is reflected off clouds. It can sometimes be seen in cirrus clouds with ice crystals and when the sun is at least 58 above the horizon.

So in conclusion, a rainbow is not just freak occurence that presents itself magically when the sun comes out while its raining, nor is it just a book by D.H. Lawrence. A rainbow is caused by dispersion of sunlight as it goes through raindrops and has been mathmetically explained by scientists and astronomers. They include the Persian astromoner, Qutb al-Din al Shirazi (1236–1311) who is thought to have first given a fairly accurate explanation for the rainbow phenomenon and Descartes in 1637 treatise, Discourse on Method, further advanced the Shirazi's explanation. We can ultimately credit these two scientists for their discoveries on the workings of our culture's fascination, the rainbow.

Works Cited

http://www.geocities.com/capecanaveral/hall/6645/Rainbow/rainBow.html
http://eo.ucar.edu/rainbows/
http://www.batesville.k12.in.us/Physics/PhyNet/Optics/Refraction/Rainbows_2.html

The Physics of a Rainbow



So some of you might be wondering, what exactly is a rainbow? We all enjoy spotting one in the sky on those rare occasions but few of us know why it got there in the first place. A rainbow can be described as a charming chromatic dispersion. It is formed when white sunlight is intercepted by a drop of water in the atmosphere and some of the light refracts into the drop, reflects from the drop's inner surface, and then refracts out of the drop. The first refraction separates the first refraction separates the sunlight into its component colors and the second refraction increases the separation ultimately resulting as a rainbow. Colors of a rainbow are caused by the refraction and internal reflection of light rays that enter the raindrops. The concentration of rays near the minimum deviation gives rise to the arc of the rainbow. The incoming ray is unpolarized, and can be represented by two polarized waves whose plans of polarization are perpendicular to each other. There a few things that can happen to the ray when entering atmosphere. Part of the incoming ray is reflected back to the atmosphere; part of the light refracts into the drop and then refracts back to the atmosphere; some reflect from the drop’s inner surface and refract back to the atmosphere. Ultimately this refraction of rays give rise to an ordinary rainbow. In some cases, some rays will reflect twice inside the drop and then refract back to the atmosphere which ultimately gives rise to a secondary rainbow.
Rainbows briefly can be described as an optical and meteorological phenomena which cause a spectrum of light to appear in the sky when the sun shines onto droplets of moisture in the Earth’s atmosphere. As a result one can see a multicolored arc with red on the outside and violet on the inner arc. In most cases the spectrum of colors usually result in a sequence of Newton’s sevenfold red, orange, yellow, green, blue, indigo, violet or also known as Roy G. Biv.
A secondary rainbow can be seen on rare occasions outside the primary arc with colors in the opposite order. Though rainbows are usually bow-shaped, there are also phenomena of rainbow-colored strips in the sky: in the shape of stripes, circles or even flames
The rainbow is actually a disk of scattered light, but it is brightest at the edge; the disk for different wavelengths is a different size, and that is why we see the color effects there.When light refracts, it follows the law of refraction ni sin(ctai)=nr sin( ctar) where n is the index of refraction. There is an angle of incidence and an angle of refraction. Most of the light is refracted out by one ray. When your eyes intercept the separated colors from the raindrops the red color you experience is the product of when drops are angled slightly higher in the sky than when you experience seeing blue. The overall effect is that the incoming light is reflected back over a wide range of angles with the most intense light at an angle of 40-42 degrees. The angle is independent of the size of the drop but does depend on its refractive index. For instance, seawater has a higher refractive index than rain water therefore the radius of a rainbow in the sea spray is smaller than an actual rainbow. It becomes visible to the eye due to a misalignment of these bows.

The case Brown versus Board of Education was significant because it stuck down the "separate but equal" doctrine of the Plessy vs. Ferguson case. The Brown vs. Board of Education court case was over a young black girl named Linda Brown who was forced to walked a mile to a black school everyday rather than seven blocks to a white school. The NAACP got involved in the case and said that segregation was harmful to the education of black children because it made them feel inferior to whites and therefore were unable to learn. The Board of Education defended segregated schools and said that the segregation of schools prepared children for the reality of life because everything in society is segregated between whites and blacks at the time. In addition the precedent of the Plessy vs Ferguson case was set and therefore the Supreme Court was leaning more towards the Board of Education but after further review Chief Justice Earl Warren announced the unaminous decision to rule in favor of the plaintiff. The Supreme Court stated that they believed although tangible factors may be equal between the two that separate education facilities are unequal. This decision did not abolish segregation in other public places however it did declare the permissive or mandatory segregation in schools unconstitutional.

LAD # 29

President Truman addresses that Greece is asking the US to aid its country economically. Greece is not a rich country and it lacks sufficient resources to keep the country from being occupied from foreign invasion. It hopes that with finincial aid from the US it will be able to avoid falling to Communism and will be able to establish a democratic government that is stable. The country of Greece is in desperate need of financial and economic assistance in order to enable it to resume purchases of food, clothing, fuel and seeds. It has specifically asked for help from the United States rather than the United Nations because of their need for immediate help. The country is constantly threatened by communist groups and unable to protect itself because of its small and poorly organized army. Greece's neighbor, Turkey also deserves attention as well according to Truman. Aiding Turkey is essential to the preservation of the Middle East therefore we must provide them with economic and financial aid as well. It is the duty of the United States to prevent countries from falling from the choice of democracy into a communist government. By helping these countries the United States will be giving effect to the principles of the Charter of the United Nations. According to Truman, if Greece should fall into Communism the immediate effect would be that Turkey would fall too and then continue to spread throughout the Middle East. Therefore Truman asks Congress for $400,000,000 to aid Greece and Turkey and also American to provide American civilians and military personel in the countries as well. If the US is to falter in our leadership role it is possible the the world may be endangered, including endangering the welfare of our own nation.

LAD 28

IN Franklin D. Roosevelt's inaugural address he announced his plan of the New Deal. He states that there is concern in the nation that taxes have rises and the ability to pay has decreased, farmers have no market and savings of thousands of families have been lost. In addition, unemplyment is common and he wishes not to deny any of these things and to be truthful. FDR calls for a restoration of ethics and action by the nation. The first task he faces is to put people to work. FDR calls for strict limitation on credit and banking and an end to speculation of money. He goes on to say that everyone in the nation must work together and be a good neighbor. It is times like these that prove how people are interdependent on one another. Furthermore, he is aware that the nation faces an unprecedented trama therefore he is is willing to adapt the political power of the legislative, judicial and executive branch in order to pursue restoration. He accepts his role as the leader "of a great army" and will take direct and vigorous action for the arduous days ahead.

LAD 28

IN Franklin D. Roosevelt's inaugural address he announced his plan of the New Deal. He states that there is concern in the nation that taxes have rises and the ability to pay has decreased, farmers have no market and savings of thousands of families have been lost. In addition, unemplyment is common and he wishes not to deny any of these things and to be truthful. FDR calls for a restoration of ethics and action by the nation. The first task he faces is to put people to work. FDR calls for strict limitation on credit and banking and an end to speculation of money. He goes on to say that everyone in the nation must work together and be a good neighbor. It is times like these that prove how people are interdependent on one another. Furthermore, he is aware that the nation faces an unprecedented trama therefore he is is willing to adapt the political power of the legislative, judicial and executive branch in order to pursue restoration. He accepts his role as the leader "of a great army" and will take direct and vigorous action for the arduous days ahead.

LAD #27

The Kellogg-Briand Act of 1929 was a treaty between the United States and the other powers. It was a treaty that stated that any power who wanted to seek interest in terms of war should be denied of the pact. This was done in order to encourage by example to other nations of the world to adhere to the Treaty. Article I stated that High Contracting Parties should condemn the concourse of war in relation with one another. Article II stated that if problems should ever arise between any of the nations that it will only be dealt with by pacific means. Article III says that the Treaty should be put into effect once it is ratified. It became effective July 24, 1924.

LAD 26

The Schenck v. United States was an indicament on three counts. The first count being a conspiracy to violate the Esionage Act of June 15, 1917 by causing insubordination in the military and navy. Also the obstruction of recruiting and enlisting services during a time of war with Germany with the sending of mailed documents to those drafted by the Act of . the defendants printed and mailed documents by the Act of May 18, 1917. The second offense was the conspiracy to commit a federal crime against the United States. The third was the mailing of things that were unmailable. Schenck was a socialist leader who circulated flyers to recently drafted men and cited the Thirteenth Amendment which was against "involuntary solitude." The Conscription Act was a result of the resistance. Schenck was convicted of violating the Espionage Act and the justice declared his conviction constitutional. Justice Holmes then sets up the "clear and present danger" and announced that it was inappropriate to yell "Fire!" in a movie theater.

LAD # 25

Woodrow Wilson's Fourteen Points was delivered to Congress on January 8, 1918. Spokesmen of the Central Powers have indicated they a desire to establish peace towards the Russians. Represents have been present at Brest-Litovsk and the Russians came up with definite principles of peace while the Central Powers came up with an outline that allowed no concessions of land. Russian representatives dismissed this plan. Due to the lack of compassion that Germany and the Central Powers held toward Russia, Russia remains powerless. Although in a grim situation, Russia does not yield its principles and honorable ideals. Therefore, the US must enter the war because of the violations of rights by the Central Powers and a desire for world peace. A program of the world's peace has 14 points to it.

I) Diplomacy must always be in a public view
II) The seas must remain free in times of both peace and war
III) Removal of economic barriers and the establishment of equality of trade conditions for all nations consenting to peace.
IV. National arms should be reduced to the lowest point that still allows domestic safety.
V. An adjustment of colonial claims is to be made
VI. The evacuation of Russia by other countries
VII. Belgium must be evacuated and restored and allowed unlimited sovereignty.
VIII. French Territory should be freed and the invaded portion restored.
IX. The frontiers of Italy should be lined according to nationality.
X. Austria-Hungary should be allowed to pursue autonomous development.
XI. Rumania, Serbia and Montenegro should be evacuated and restored
XII. The Turkish portion of the Ottoman Empire should have a secure sovereignty while the other nations under Turkish rule should be allowed autonomous development.
XIII. An independent Polish state should be established and assured free and secure access to the sea.
XIV. A general association of nations must be formed in order for nations to communicate political issues.

In conclusion, the program asks governments associated against Imperialists to unite in a purpose for peace. Wilson makes clear that the US is not jealous of Germany's greatness and the US does not wish to fight her with arms. In addition, the US does not wish to change any institution of Germany's and all that the US asks of her is to accept a place of equality instead of mastery among the world. The program itself is based on the principle of justice. Without justice, there would be no structure to international justice; the US will act upon no other principle other than justice.