Finding the Focal Length of a Lens Essay Example

Finding the Focal Length of a Lens Essay Lenses have fascinated physicists ever since well they have fascinated Mr. E. Allen so thats more than enough.Anyway, lenses can be used to modify images in a number of ways. They can be used to focus, blur, enlarge, reduce (which is still technically an enlargement with a factor less than one) and flip an image upside-down.With all of these properties, there must be some rules governing how a lens works. In physics this means there are some mathematical rules, which can be shown through equations. For lenses, there is the lens equation, which states that when the image is focused:u Object to lens distancev Lens to image distanceà ¯Ã‚ ¿Ã‚ ½ Focal lengthThe Lens Equation (2)There is also another equation relating the focal length of a lens to the power of the lens:and thusP Power of a lens in dioptres (D)à ¯Ã‚ ¿Ã‚ ½ Focal length in metresIf we know the power of a lens, we can work out the focal length and likewise, if we know the focal length we can work out the power. Once we have the focal length of a lens, we can work out the object-lens distance and/or the lens-image distance through the lens equation.There is even more. We can also work out the enlargement factor between the object and the image by drawing ray diagrams.Ray Diagrams (3)Armed with all of these techniques, we will hopefully be able to find the focal length of a lens.The PlanIn this experiment (derived form Activity 23), the aim is to use the lens equation to find out the focal length of a lens. I have been issued with a 5D (5 dioptre) lens. From the power equation we can work out the focal length to be:à ¯Ã‚ ¿Ã‚ ½ = 1/Pà ¯Ã‚ ¿Ã‚ ½ = 1/5à ¯Ã‚ ¿Ã‚ ½ = 0.2 m (20 cm)To verify that the (principal) focal length is 20 cm, I will need to do some experiments. As Activity 23 is the basis of this investigation, its a good idea to follow what it asks. However, before I conduct the experiment, I will pre-test Activity 23 to see if there are any possible problems.Activity 23 suggests that we use a coloured light source and a lens with which we can focus the light onto a screen.Activity 23 Apparatus Set-up (1)As the object-lens distance (u) and the lens-image distance (v) i.e. the lens-screen distance were altered, some interesting things happened.* The red and blue light are flipped vertically (upside-down). This can be explained through the use of a ray diagram as seen on Pg 2.* The red and green light did not focus at the same points; therefore the focal length is dependant on the wavelength and/or frequency of the light.* When one of the coloured lights was focused, it wasnt focused at a single point, but over a range of distances (u and v). This means that the focal length cannot be pinpointed. Instead, we get a mean for the focal length with some uncertainty/deviation.* Because the light was in a shape of a circle, it was hard to distinguish a point where the dot was focused. A sharp-edged light source (e.g. a square) would have been more helpful as it would have been e asier to see if the edges were in focus.* The object-lens distance must be greater than the focal length of the lens; otherwise a magnification of the object occurs. This image can be projected but cannot be focused onto the screen (this image is known as a virtual image).* However, this effect became useful, because we used another lens to magnify the image on the screen to see whether or not the image (dots) were in focus. (See third bullet point)After doing the pre-test, the problems encountered can be rectified in the experiment proper.Now all that is left is to make some measurements of u and v when the image on the screen is focused, put them into the lens equation and see whether or not the focal length is 20 cm.The Method1. Gather the required equipment: A lens, paper (to act as a screen), a stand to hold the screen, a double light source (plus power pack).2. Align the light source, lens and screen. Then focus the image from the light source onto the screen for the red light . To ensure that the image is focused, use another lens to magnify the image that is on the screen.3. Measure the distances for u and v and record the results.4. Repeat steps 2 ; 3 for the green light.The Safety (Issues)Although this is a relatively safe experiment, some precautions should still be taken. If the experiment was to be carried out on the floor, then precautions must be taken to prevent people from tripping over the equipment.Also, when supplying the lights with electricity from the power pack, it is better have a low voltage setting as this reduces the risk of the light source burning and the extremely unlikely possibility of setting the whole science block of fire!The Results(See Results Sheets)The AnalysisThe results show that the focal length of the lens is around 20 cm (200 mm). However, the (average) focal length is not exactly 200 mm, which suggests that either there is an error in the experiment or there is an error in the lens. More precisely, there is a possib le error in the way the power of the lens was calculated by their manufacturer.As I found out in the pre-test, different coloured light has different focal lengths. The speed of light in any specific medium is constant. As the wave equation says:v Velocityà ¯Ã‚ ¿Ã‚ ½ Frequency? Wavelengthand the frequency of light didnt change, or at least not a noticeable change (as the frequency of light determines its colour), only the wavelength of the rays changed could have changed as they went into the lens.The focal length of the lens was longer when the red dot was focused that it was when the green dot was in focus (See The Results Section). This shows that the focal length is inversely proportional to the frequency of light used (as green light has a higher frequency that red light).This also shows that the refractive index between any two materials is dependant of the frequency of light used. This can be shown if we simplify the shape of the lens used in the experiments. (4)(NOTE: Di agram not necessarily to scale)To begin with, the angle of incidence is the same with both rays. However the different light rays are refracted at different magnitudes and so the refractive index must be different for the two rays. Notice how the focal length are different, and this must have resulted from the theory that the refractive index is dependant of the frequency of light used because the same lens was used to focus the two different coloured dots.Moreover, the refractive index must be directly proportional to the frequency of light being used. This can be explained by the use of further diagrams.(NOTE: Diagram not necessarily accurate or to scale, and parts are exaggerated for the purpose of emphasis)As we saw earlier, the green light was bent more by the lens that the red light (and yes I know bent is a loose word, but its the best I can think of). This basically means that the angle of refraction, r, is smaller for the green light than it is fro the red light. Since Snel ls law states that:if the angle of refraction, r, is decreased, the denominator (sin r) becomes smaller and therefore making the whole fraction bigger. This is true when green light is used instead of red, as the angle of refraction is smaller with green light than with red light (while the angle of incidence, i, is the same for both colours). This means that the green light has a bigger refractive index than the red light. In conclusion, the refractive index is directly proportional to the frequency of light used.So, we have established that the refractive index and therefore, the focal length of a lens are dependant on the frequency/wavelength of the light used.(Phew!)In order for manufacturers of lens to measure the focal length of lens, they must have a standard frequency for which the focal length of a lens is measured with. From my results, the frequency used to measure the focal length is above the frequency of green light. As the lens used in the experiment was a 5D lens, th e focal length must be 20 cm (200 mm).My results show that the focal length decreases as the frequency of light increases (i.e. focal length is inversely proportional to the frequency of light used). They also show that the focal length of a 5D lens, when measured with red and green light, is more that 200 mm. This leads me to conclude that when the manufacturers measured the power of the lens, they must have used a light with a higher frequency than that of green light. Since the power of the lens is 5D, the focal length should be 200 mm, and the only way for the focal length to be 200 mm is to use a higher frequency light source.The EvaluationAs mentioned earlier, having a shaped light source would have made the experiment a lot more accurate than they currently stand.

Farther and Further - Glossary of Usage

Farther and Further - Glossary of Usage Farther usually refers to physical distance. Further refers to an extension of time or degree. But see the usage notes below. Examples We drove farther south, making excellent time on the almost empty roads.The meeting ended without any plans for further discussions.We traveled farther in one week than any of us had expected. The trip took us even further into debt. Usage Notes Since the Middle English period many writers have used farther and further interchangeably. According to a relatively recent rule, however, farther should be reserved for physical distance and further for nonphysical, metaphorical advancement. Thus 74 percent of the Usage Panel prefers farther in the sentence If you are planning to drive any farther than Ukiah, youd better carry chains, and 64 percent prefers further in the sentence We wont be able to answer these questions until we are further along in our research. In many cases, however, the distinction is not easy to draw. If we speak of a statement that is far from the truth, for example, we should also allow the use of farther in a sentence such as Nothing could be farther from the truth. But Nothing could be further from the truth is so well established as to seem a fixed expression.(farther, The American Heritage Dictionary of the English Language, 4th ed., 2000)Farther and Further are historically the same word, so it is not surprising that the two have long been used more or less interchangeably. . . .As adjectives, both words could at one time be used in the sense additional. . . .But in present-day English further has taken over this use entirely. . . .Farther has been relegated as an adjective to instances where either literal or figurative distance is involved. . . .And even in this function further is presenting formidable competition. . . .So for the adjective we can see that further has squeezed farther out of the additional sense and is giving it considerable pressure in the more distant sense. . . .In adverbial use further dominates when there is no sense of distance and as a sentence adverb, but both farther and further are in flourishing use whenever spatial, temporal, or metaphorical distance is involved. (farther, further, Merriam-Websters Dictionary of English Usage, 1994) No one misuses farther for further, and youre safe with further provided that you dont apply it to distance. Several usage critics have even predicted that further will eventually absorb the meaning more distant, driving farther into extinction. (Claire Kehrwald Cook, Line by Line: How to Edit Your Own Writing. Houghton Mifflin, 1985) Practice (a) We need to explore this problem ______. (b) Simon walked ______ into the woods. See Also Avoid These 10 Words in Formal Writing.Glossary of Usage: Index of Commonly Confused Words Answers to Practice Exercises (a) We need to explore this problem  further. (b) Simon walked  farther  into the woods.

Literature Essay Example | Topics and Well Written Essays - 750 words - 5

Literature - Essay Example However, the real test of creativity and brilliance comes when a person shows creative abilities while remaining in the boundaries of conventions and rules which are set forth for the medium being used. Making things different is not breaking conventions since a broken convention is nothing more than ignoring a long standing rule. Creativity can be reflected in the application of the same rule in a different way going as far as altering rules to produce something which is beautiful because it is imperfect. For example, Shakespeare used the words, ‘most unkindest cut’ which is a grammatically incorrect phase but certainly shows the emotion and feelings of the characters in Caesar. It goes against the conventions of writing but this makes the phrase stand out from many others. In fact, this is not the only time Shakespeare broke away from conventional writing and produced something which has stood the test of time as an example of a masterpiece. For instance, some sonnets of Shakespeare go against several rules followed by sonnet writers in the Jacobean era even though Shakespeare himself was responsible for creating many conventions followed in the same times. His work, Shall I compare thee to a summer’s day is a perfect example of a conventional sonnet by Shakespeare. The sonnet has four stanzas with three quatrains, the final couplet is composed in iambic pentameter and the rhyme scheme is perfect as abab cdcd efef gg. In fact, the system used for such sonnets have come to be known as the system for Shakespearean sonnets (Wikipedia, 2006). It is commonly accepted as one of Shakespeare’s most beautiful sonnets because it does not break any conventions but comes out as a very creative and different effort from the rest of the poetry by the bard. Shakespeare does not always play by the rules set out by him and can offer variations and changes depending on how he wishes. In a few other sonnets, there are significant departures made from

DiSC Personality Sssessment Research Proposal Example | Topics and Well Written Essays - 750 words

DiSC Personality Sssessment - Research Proposal Example How important is it that a persons' DISC Profile match up with the perceived needs of a particular job I wish to address this problem specifically within the context of a teacher's perception of a secondary principal in his or her role of leading teachers through the change process. This could serve as a useful tool in improving the performance of a secondary principal or even help in defining the actual expectations for a particular position. From this basic research, many more meaningful studies could come about. The problem is that we wish to understand what teachers need from the secondary principal in terms of DISC traits and if these perceived needs have the potential to be fulfilled within the actual relationship. We could discover if it is in some way helpful to use the DISC Profile in identifying future candidates and delineate which particular qualities in the candidate make them most appropriate. The study could be used as an aide to modify the performance of an existing principal by identifying key areas for improvement. The purpose of the study is to determine if there is any correlation between a teacher's perspective of DISC Profile personality traits of an ideal secondary principal and the actual results of DISC analysis of a secondary principal... One provocative theory is that the teachers know best about which personality traits a principal must possess in order to achieve success in leading them through the change process. In an ideal situation, these expectations would be fully realized during the change and correlate closely with the actual DISC assessment of a successful principal. This is the most tempting possibility because it is the simplest and most straightforward. It lends credence to the idea that there is a high degree of correlation between expectations and outcome. When the project is moving along according to plan, then it is an excellent indicator that all is well. Further investigation is required only when the performance is unsatisfactory. The DISC analysis is a useful tool because it is geared towards self-improvement and personal growth. In this study, discrepancies between actual and perceived DISC traits could be revealing in such a way that would allow a secondary principal to achieve his or her full potential. If from a teacher's perspective a secondary principal was lacking in some critical personality trait and this conflicted with his or her DISC Profile, then that might indicate the capacity and need for change. The DISC Profile could act as a common ground between all of the individuals involved in the process and provide direction for increasing the effectiveness of the project as a whole. The methodology of this research study would involve the distribution, collection, and analysis of a DISC type personality trait inventory sent to teachers and comparison of these inventories to an actual DISC Profile completed by the secondary principal. As a model for the study, one local high school would be selected to participate based on interest and the ability to

The Great Depression and President Roosevelts New Deal Assignment

The Great Depression and President Roosevelts New Deal - Assignment Example There were factories then and employment was in blossom. This was however reversed when the market crashed because the era of Great Depression followed suit. The Great Depression had the effect of reducing the majority of the people in America to become paupers. President Roosevelt had to introduce drastic policies to reverse the tide for America to get back at its feet again. The New Deal involves many economic policies that were centered on giving relief, reform, and recovery to end the Great Depression. This policy mandated the opening of banks so that business can flourish. The government became an employer through Works Progress Administration (WPA) programs so that people can have jobs and income. He also pumps prime the economy by spending a lot of money in building infrastructures. Little by little, America recovered (www.history.com). The New Deal proved to be effective as it did not only end the Great Depression but made America as the strongest economy in the world (The New Deal). From being paupers with nothing to eat during the Great Depression to become the most affluent country in the world. This happened after the war where war expenditures multiplied America’s GNP that contributed to its meteoric rise after the Great Depression. The positive effect of Great Depression and New Deal on America’s lifestyle is that it taught them resilience and to value hard work to achieve anything and even to become the strongest country in the world. The negative effect, however, is that the people became too materialistic and too selfish as they try to compensate for their hardship during the Great Depression. The New Deal did not only employ the artist, musicians, actors, and writer but in fact everybody to put money in the system. It has to be remembered that the New Deal also spent a great deal on infrastructure and this required a huge number of workers.  

A Comparison of Tom Regan and Stephen Rose

A Comparison of Tom Regan and Stephen Rose Brianna Still People often use animals for a lot of experiments even though most people think that is it wrong. People make up countless excuses to why its okay to do this. But it is not okay. Animal researchers and such agree with my opinion that using animals for tests that we as humans would never want to do, is bad and very hypocritical, yet unfortunately there are just as many scientists who say that it is completely fine and that there isnt really much harm brought to the animals. Mind you, these scientists have apparently never owned a beloved pet close to their heart. The two essays, Animal Rights, Human Wrongs by Tom Regan and Proud to be Speciesist by Stephen Rose, talk about the issue of animal rights, but are written on completely opposing sides. They both talk about animals that are used for human benefits but in two completely different ways. Regans essay is much wider in my opinion. Roses essay looks at a detailed and personal view in this subject matter. Regans argument is that ani mal usage should be stopped because animal experiments for humans is not justified. But, Rose challenges Regans idea saying that the safety of mankind is more important than the rights that we would like animals to have. He says that using animals for research is perfectly fine. Regan is better at explaining the subject and has more credibility with actual examples to give a whole image of the subject matter. Rose doesnt do so good because his material is only built from science and research. Regan just appears more logical and fair on the issue matter. According to Regan animals have ethical rights, so he states that he thinks that they should be treated with respect by sane humans. He talks about how a mans description about the whaling process to show how few rational humans killed a whale for their ravenousness (336). Regan happens to be a philosophy instructor, therefore the arguments and viewpoints that he makes are more trustworthy. For a long time, hes been quarreling for the rights of animals, thus his statements are supported with very sturdy reasoning and they are sourced from all types of fields from things like people, knowledge and science. He states that butchering animals for pleasure, luxury and experiments is not at all right or vindicated, so it shouldnt be practiced. Regan claims that if it cannot be justified, then it shouldnt be done. Of course most people and organizations that do these type of things cannot come up with a moral enough reason as to why what there doing is actually justifiable, hence he probes them to stop using these creatures unless they can deliver a fitting justification. On the opposing side, Rose discusses the prominence (and therefore, importunateness) of animals when it comes to research and exploration for the physical wellbeing and survival of people. He quotes Alzheimers as an example (342) from his own particular experience to illuminate the role that animals play in human research to find treatments for it. Roses arguments about animals rank in research are undisputable because these claims are backed up completely by logic and science. Rose, himself is a biology instructor and a researcher on the side, so his arguments are very much reliable, usable and logical. He says, The first statement is plain wrong; the second, the claim that animal have rights, is sheer cant (342, 343). Moreover, he speaks about speciesism and states that animal activists are speciesists too; they just prefer animals to humans. Though his arguments are solid, his credibility is weakened because his aims and examples are only from science. Also, his biasedness can be taken into consideration, because he is a researcher, not an activist. He doesnt care as much about the moral rights. Even though the practice of these beasts in research is essential, his opinions and arguments are weak because of the narrow space of his research. Regan has carried on about how science constantly ignores animals rights. He declares that the research on animals are just not justified sufficiently, and he thinks that using animals for our welfares is ridiculous. Regan talked about a rabbit in stock (337) to show how a rabbit is put through many pains just to find out the feasibility of cosmetics and such on people. Yet this example of the rabbit supports his idea, it doesnt shield the entire idea of research. Some researches about deadly diseases are unavoidable because they are vital to the survival of human life. Regans argument is still weak since he isnt able to describe exactly why this research cant be avoided. In total, Regan sounds pretty convincing, and his philosophies are pretty much effective regardless of occasional drawbacks. Rose clarifies how scientists have been able to find cures for things like Epilepsy, Parkinsons, diabetes, and such (343), and he talks about how fundamental animals are in that research. He says, How far the concept of right can be extended-to not swatting a mosquito that is sucking your blood? To prevent your cat from hunting and killing a rat? Does an ant have as many rights as a gorilla? (343). Rose additionally indicates that some species of are more privileged than others if that species is more important than the other one. He talks about the rights of animals being only relative, meaning that if animals are in a greater proximity with human than they have more rights and vice versa; if we are in more proximity than we are the ones with more rights. He feels that activists of animal are Speciesist themselves, so he its not wrong if its vice versa as anti-activists are speciesist too. He says, Just because we are humans, any discussion of rights must begin with human rights. (3 43). Rose is proud to be a speciesist in favor of humans since he thinks we should privilege humans over animals and he, himself is a human. Roses urgings and examples are pretty convincing and full of facts, but they keep being weakened by doubt about his limitation. Roses reasoning and good logic can also be flawed by arguments that are from every other field except actual science. Hence, Roses idea gives room for some doubt although his reasoning, facts and ideas about the research are very waterproof. Regans tactic for the topic is fair. He started somewhat aggressive, but then considerate and lastly suggestive. He says, Possibly the rights of animals must sometimes give a way to human interests (339). He knows that usage of animals for the happiness of humans, from time to time, cannot be completely rejected, but all he asks for is a legit, logical reason. He states that all cruel things done to animals should be justifiable, otherwise they shouldnt even be considered valid. Then, he suggests a relative approach of how a deed can be justified with an example of racism and sexism (339). He asked people to reduce animal use as much as they possibly can, and justify it every time they kill an animal. His hint of relative approach pleases the readers conscience and is able to leave an impact on readers mind. Rose, conversely, says that there are not any rights that are not as privileged as humans. His awareness of our human rights alongside animal rights calls the integrity of the readers. He mentions that animal activists are speciesist too, so we too can be speciesist of humans. Rose says that animal activists are the kind of people who take medicine for Parkinsons disease, for example, or insulin for their diabetes, and such although they know that those drugs or treatments were experimented on animals. Roses reasons are faultless, but overlooks that it is a normal human behavior to aid an illness with prescriptions and medicine. Any rational thinking being would do anything for the certainty of their survival, so his argument can be questioned if you put it in that light. Rose talks about Declaration of Animals in Medical Research (344) that is only signed by specialists and doctors, and not by other fields of people. Thats why, while Roses opinions about speciesism in favor of human s are reasonable, sound and considerable, his notions are weak because he is so narrow and bias. Regan effectively presented his notions, reinforced by legit factual evidence, lecturing all likely parts, whereas Rose built his thoughts on facts and examples solely from research and science and that made him that much less credible and it made his arguments narrow. Roses statements and ideas can be effortlessly weakened rather than Regans arguments, because there are definitely potential doubts about his biasedness, and also his arguments are just really narrow. Though Rose made some very solid points in his essay, he could have been a lot more effective, and Regans essay contains just about everything and talks about the obvious wrongs that the rest of us cannot and should not ignore. Works Cited Regan, Tom. Animal Rights Human Wrongs: An Introduction to Moral Philosophy. Rowman and Littlefield Publishers, 2003. Rose, Stephen. Proud To be A Speciesist.

Censoring the Pages of Knowledge Essay -- Books Literature Essays

Censoring the Pages of Knowledge Imagine a world where you could not read or own any books. How would you feel if you had someone burn your house because you have books hidden within the walls? One of the most prevalent themes in Ray Bradbury's novel Fahrenheit 451 is the idea of censorship. In Bradbury's fictional world, owning books is illegal. A fireman's job is not putting out fires like one may assume. In Fahrenheit 451, a fireman has the job of starting fires. Firefighters start fires in homes containing books. If this were reality, there would be no homes to live in. Books have become an integral part of American life. However, the theme of censorship is still relevant in American life. Censorship is enforced in an interesting way in Fahrenheit 451. Normally if someone was asked about the roles of firemen, they would respond, "firemen are people who put out fires." The role of firemen in Fahrenheit 451 is completely different. Firemen are the enforcers of the censorship laws. They are called upon when a person is known to have books in their house. The opening line of Bradbury's novel is, "It was a pleasure to burn" (3). Firemen seemed to enjoy their status as book burners. Many even got an adrenaline rush out of burning books. Guy Montag, the protagonist and main character of the novel was a fireman who once felt starting the fires in people's homes was thrilling. In describing Montag's actions during one particular fire, Bradbury writes, "He wanted above all, like the old joke to shove a marshmallow on a stick in the furnace, while the flapping pigeon-winged books died on the porch and lawn of the house" (3). This quote demonstrates the mentality of the firemen an d the opinion of the government. Books are evil in t... ...in restrictions are needed. Pornography should not be available to children. I do not have a problem with parental advisory labels on music. However, putting a ban on all books is a very scary proposition. Bradbury's novel does not come close to describing how miserable this world would become. Everybody in this world depends on books whether or not they are literate. It can be said that we get most of our morals and values from books. These morals are found in books such as the Bible, Aesop's Fables, and sometimes even the trashy romance novels that women tend to love. Without books, the world could be explained in one word, educated. An uneducated world is a miserable world full of fighting and conflict. An uneducated world is a world at constant war. A world with out books is a dystopian world. Bradbury, Ray. Fahrenheit 451. New York: Ballantine Books, 1953.