Beer-Lambert’s Law Experiment

Beer-Lambert’s Law Experiment Design Project on  Beer- Lambert’s Law. Saswati Rakshit Aim: To learn and understand the basics and mathematical calculations of the following problem and write programs accordingly. Problem 1: Suppose an outdoor multispectral image is captured by a camera with a path length of 1-3 microns. A part of the intensity is attenuated by the absorption of small particles in the atmosphere for that spectral range and let the scattering by the small particles for that spectral range is 0. Find the total attenuation in the spectral range using Simpson 1/3  ­, trapezoidal and Euler integration methods and comment in your findings. Scope/Application: Beer Lambert’s law relates the attenuation of light to the properties of the material through which the light is passing. When light passes through a medium some amount of light is absorbed by the medium. For this absorption intensity of light reduces. Beer Lambert’s law states that the quantity of light absorbed is directly proportional to the concentration of the substance and the path length of the light through the transmission medium Beer Lambert’s law is used to find total attenuation of light when light passes through a medium(considering scattering is zero).It is also used to find the concentration of medium in chemical analysis, medium length in some application and absorbance of medium when necessary. Introduction of Beer Lambert Law: Lambert’s law is (Related to thickness/path length of medium) When light passes through an absorbing medium its intensity decreases exponentially as the path length of the absorbing medium increases. I = I0 e-k1 L †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.(i) (where L is the length of medium and k1 is molar extinction/absorption co-efficient for the absorbing material) Beer’s law is (Related to concentration of absorbing medium) When light passes through medium(absorbing) its intensity decreases exponentially as the concentration of the absorbing medium increases. I = I0e-k2C †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦..(ii) (C concentration of medium and k2 is absorption co-efficient for the absorbing material) Combining both Beer’s and Lambert’s law we get I = I0 e-k3CL combining eqn (i) and (ii) Where I0 = Incident light intensity I = Transmitted Light intensity C=concentration / volume L= path length of medium We consider an outdoor multispectral image is captured by a camera with a spectral range of 1-3 microns. A part of the intensity is attenuated by the absorption of small particles in the medium.so image will be attenuated. Beer Lambert’s law find the attenuation caused by absorption for that spectral range and let the scattering by the small particles for that spectral range is 0. Objectives: In a given path length 1 to 3 micron, we have considered a constant value of molar extinction/absorption co-efficient.and now we need to find the absorbance total attenuation of the incident light using Beer’s Lambert Law. And then applying Simpson’s 1/3, Trapezoidal and Euler Integration in it compare the result. System flow: Implementation of the Beer Lambert’s law needs a proper mathematical understanding of the Beer Lambert’s law. Here I am showing how to set the equation using its mathematical basics First we apply Beer Lambert’s Law for a medium which absorbs light in spectral range 1-3 micron. Considering no scattering we assume I0 is the incident light to the medium Air of attenuation coefficient 1.64at temperature 20oC. Here path length travelled by light is 1 to 3 micron. According to Beer Lambert’s law light intensity is decreased if concentration path length increase. So we get the equation I=Io e-kcl = Io e- µl Now as we know the path length l and attenuation coefficient  µ, we calculate absorbance of the medium using eqn Log10 = kcl (Where l is constant) = e kcl But now for a spectral range 1 to 3 micron path length we need to formulate a new equation by integrating ranged from .001mm to .003 mm [Here x is path length and c is attenuation coefficient] Solving the above eqn we get total absorbance. Thus Beer Lambert’s law is successfully implemented in our problem. Now we apply Simpson 1/3 rd, trapezoidal rule on Beer’s Lambert Law to find total attenuation. Finally compare the result of Simpson’s 1/3 rd and Trapezoidal rule with the actual integration. Flow Diagram: Math: Beer-Lambert Law Concept Consider a light incident on a medium with area A and thickness dx and concentration of molecules C. Number of molecules illuminated by light of incident intensity Ix is CAdx. Total effective area ÏÆ'CAdx. Probability of light being absorbed in thickness dx is = dx [where dIx is the change in intensity across dx and ÏÆ' is scattering coefficient] So we can write, = dx †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ (i) Now we integrate both sides of (i) ln (I) – ln(I0) = ln = ÏÆ'Cx I = I0e-ÏÆ'Cx = I0 e µx †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.(ii) The co-efficient  µ=ÏÆ' C is the linear attenuation co-efficient. Here C=Absorbing co-efficient ÏÆ' = Scattering co-efficient. The ibrightness of light decreases exponentially with depth in the medium. So we can tell Beer-Lambert Law is also a function of( ÃŽ »), i.e. I (ÃŽ ») = I0 (ÃŽ ») e- µ(ÃŽ »)x†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦(iii) Calculation: (Here we considered linear attenuation) Given spectral range 0.001 mm to 0.003 mm Let we consider Absorbing coefficient(C) of Transmission Medium (Air) = 1.64 at 20o C. So total absorption (A) of light is calculated by integrating in the spectral range, [from eqn ii] = (1) = = 0.002006571 Now we can easily calculate attenuated intensity of light (I). Attenuation is the loss of light intensity over distance. The greater the distance, the lower is the intensity Where I=I0 -Attenuation Trapezoidal rule:- We know, in case of multiple application of Trapezoidal rule, the formula is: = [f(x0) + 2) + f(xn)] So, here applying the above formula for equation (1) we get: = 0.0005[[ 0.001 + 2 + [] 0.003] = 0.0005[1.001641346 + 2.00657077 + 1.004932123] = 0.0005[4.013144239] =0.002006572 (Ans.) Here, x0 = x0.001, xn = x0.003, b = 0.003, a = 0.001, n = 2, = 0.0005. Simpson’s rule: We know, composite Simpson’s rule formula is written as: = [f(x0) + 4) +2) + f(xn)] So, here applying the above formula for equation (1) we get: = 0.0003[[ 0.001 + 4 + [] 0.003] = 0.0003[1.001641346 + 4.01314154 + 1.004932123] = 0.001805914 (Ans.) Here, = 0.0003. Euler’s formula: Here, = y(0.001) = = 0 (assumption) y(0.003) = ≈ and we have to find the value of equation (1) using Euler’s formula which is, = + f (, ) h let us choose h = 0.001 Step-1 i=0, = 0.001, = 0, h = 0.001 = + f (, ) h = 0 + f (0.001, 0) 0.001 = 0.001001641 Step-2 i=1, = 0.002, = 0.001001641, h = 0.001 = + f (, ) h = 0.001001641 + f (0.001, 0.001001641) 0.001 = 0.0020049426 This is actually the value of the function at i.e. at (+h) or (0.002+0.001) or 0.003. So, = = 0.0020049426-0 = 0.0020049426 (Ans.) We find that the result of all above technique is almost same if we take approximation i.e.0.002. CODES and OUTPUT: Beer Lambert’s Law: #include #include #include int main() {float absorbtion,m,l,u; printf(nEnter spectral range); scanf(%f%f,l,u); printf(nnenter the value of absorption cofficient); scanf(%f,m); absorbtion=(1/m)*(pow(2.718,(m*u))-pow(2.718,(m*l))); printf(nnTotal absorption is %f: ,absorbtion); getch(); } Output: Simpson 1/3rd rule: #include #include #include void main() {float x[10],y[10],Total=0,h,t; int i,n,j,k=0; printf(nhow many values you will enter: ); scanf(%d,n); for(i=0; i { printf(nn x%d: ,i); scanf(%f,x[i]); printf(nn f(x%d): ,i); scanf(%f,y[i]); } h=x[1]-x[0]; n=n-1; Total = Total + y[0]; for(i=1;i { if(k==0) { Total = Total + 4 * y[i]; k=1 } else { Total = Total + 2 * y[i]; k=0; } } Total = Total + y[i]; Total = Total * (h/3); printf(nn I = %f , Total); getch();} Trapezoidal rule: #include #include #include int main(){ float x[10],y[10], Total =0,h; int i,n,j,k=0; float fact(int); printf(nhow many values of ranges you will be enter: ); scanf(%d,n); for(i=0; i {printf(nn x%d: ,i); scanf(%f,x[i]); printf(nn f(x%d): ,i); scanf(%f,y[i]); } h=x[1]-x[0]; n=n-1; for(i=0;i if(k==0) { Total = Total + y[i]; k=1; }else Total = Total + 2 * y[i];} Total = Total + y[i]; Total = Total * (h/2); printf(nn I = %f , Total); getch();} Future Work Scope: This Beer Lambert’s law can be used in image processing application where atmospheric condition is poor to find the attenuation of light and image by absorption of light. Implementing Euler Method. References: Weisstein, Eric W. Simpsons Rule. From MathWorldA Wolfram Web Resource. http://mathworld.wolfram.com/SimpsonsRule.html. (Accessed on 26.04.2015) Basics of Trapezoidal and Simpson Rules, www.math.umd.edu/~jmr/141/Simpson.pdf. Lal, A. K., Simpsons Rule, 2007, http://numericalmethods.eng.usf.edu.(Accessed on 20.04.2015) http://numericalmethods.eng.usf.edu. (Accessed on 19.03.2015) Garrett, P., Absorption and Transmission of light and the Beer-Lambert Law, Lecture 21, 2006, www.physics.uoguelph.ca/~pgarrett/Teaching.html. (Accessed on 26.04.2015) Mudakavi, J. R., Modern Instrumental Methods of Analysis, Lecture – 07, Ultraviolet and Visible Spectrophotometry – 3 Theoretical Aspects, http://nptel.ac.in/courses/103108100/7  (Accessed on 26.04.2015). www.chemwiki.ucdavis.edu. (Accessed on 19.03.2015)

Analysis of Hawk Roosting

Analysis of â€Å"Hawk Roosting† Hawk Roosting is a poem written by Ted Hughes (1930-1998). Hughes was a British poet who often described the destructive aspects of animal life, survival instincts and the brutality of nature. His poem Hawk Roosting deals with the themes evil, power and human nature told from the point of view of a hawk. This poem therefore coheres with Hughes’ other work. In my analysis I will be focusing on a characterization of the first person and what this hawk symbolizes.I will also be mentioning the message of the poem and end the analysis with a contextualization, where I also will be answering and commenting on the two following questions; â€Å"Is man fundamentally evil or good or do we all posses both elements? † and â€Å"What triggers evil? What prevents it from surfacing? † I would like to start my analysis with a characterization of the main character and the symbol of that character. This poem is told in first person through the eyes of a hawk.We are not told directly in the text that it is a hawk but we know this partially because of the title of the poem â€Å"Hawk Roosting† and somewhat because of the description we are given of the main character (the I). We are informed in stanza 1 that the main character is sitting on the top of the wood[1], which could indicate a bird or a rodent (i. e. squirrel or chipmunk) of some sort. The main character also has a hooked head and feet, which still could insinuate both bird and rodent. The reader is however convinced that it is a bird by use of the sentence;†The air’s buoyancy†¦Ã¢â‚¬  which tells us that it can fly thus it is a bird.If not for the title one could still assume it was a bird of prey as we are told that it kills[2]. Hughes uses the simple present tense to describe what the hawk is doing; â€Å"I sit, I kill†[3] with the effect that we understand that this is what the hawk does every day and that it is not an unor dinary circumstance but a regular situation. A hawk is a bird of prey, a predator, a majestic bird and it is at the top of its food chain. It has the power â€Å"I kill where I please because it is all mine†[4], and it sees itself as perfect because it is the final product of evolution â€Å"It took the whole of creation to produce my foot, my each feather†[5].The hawk is nature at its purest intent because there are no lies or arguments in this poem there is simply the truth about the nature of the hawk. Hughes points this out firstly by using the sentence â€Å"No falsifying dream†[6] and secondly by the sentence â€Å"There is no sophistry in my body†[7]. When people dream it is often of a consorted reality where anything can happen, because it is your imagination. A dream is often something you desire or can’t face in the real life, so one lives it through in a dream. A dream therefore consorts your reality or falsifies it.This Hawk does not dr eam of things that are not real. It only dreams about specific things that are a part of its reality. Sophistry is false reasoning intending to deceive. The hawk therefore only tells the truth and explains reality and how things are, no arguments just facts. The hawk knows what it is and is content with that. I believe that the hawk represents the truth behind human nature. How humans deep down are instinctive creatures and that there is a primitive evil in all of us. I believe this because the hawk is like us at the top of the food chain, the ultimate creation and it is driven by power.The only difference really is that the hawk is excused of committing evil deeds because it is its nature and it is therefore acceptable. Humans on the other hand have morals, ethics and a society which holds these norms in place and an act of evil is therefore unforgivable and non relatable. In stanza 6, line 2 the hawk also states that nothing has changed. I think this is referring to the true natur e of humanity, which is to a certain extent evil, and how it has always been a part of the human kind and it will always be a part of us. Even though humanity has become better over time (e. the Middle Ages) it is only due to societies with norms, rules and values which without, one would quicker descend into evil. I believe the message of this poem is that the nature of humankind never changes and evil is a part of us, just waiting below the surface, where if pressured, we will show our true nature. I would like to end off my analysis with a contextualization and a comment to the mentioned questions. I thing this poem has a lot in common with the article â€Å"Bad or Mad†. In â€Å"Bad or Mad† it is discussed what defines evil where they distinguish between natural and moral evil. Moral evil is defined as the evil humans do, by hoice, knowing that they are doing wrong; and natural evil is the bad things that just happen such as natural catastrophes. I would like to wi den the term natural evil to comprehend the evil acts of animals as well. The hawk is an animal and kills because it must to survive and it would therefore belong to the natural evil. However, the hawk is a symbol of the natural/instinctive evil that is in all mankind, which is harder to define. If man commits evil acts we see it as moral evil, because they have chosen to do so out of lust, fascination or even for fun in some cases. On some level the humans are exactly like the hawk.If you took away society and said every man/woman for themselves, you would have chaos and people would do whatever it took to survive. I have thereby already answered the question; â€Å"What triggers evil? What prevents it from surfacing? † I agree with Hughes’ opinion that we all have evil inside of us but it would be defined as natural evil or the will to survive which one would not necessarily depict as evil but simply the human nature. To point it out I believe that this so called evi l is triggered if you are threatened or as a result of the fear of losing your life or a loved one etc. This answer is one side of it.Another thing that has been seen to trigger a certain level of evil is power. The hawk as mentioned also symbolizes exactly that. The Zimbardo experiment is an example of power taking over and of course the lack of a society with norms which I believe is one of the main reasons that why evil does not normally surface. In murder cases where the plaintive committed the act out of grief or rage (emotions) they are penalized less because most people can relate to it and you are not fundamentally evil as for a planned murder where you could get into a more black and white conversation about good and evil.As for the question; â€Å"Is man fundamentally evil or good or do we all posses both elements? † I have to some extent discussed this but I will lay it out further. I believe that everyone has the capacity to commit evil acts if they are pushed to their furthest limits and boundaries but I would not like to think of myself as a cynic and say that man is fundamentally evil. I believe that we posses both elements and that we are capable of both.I think that is one of the main differences when one talks about evil in for example animals and humans. The fact that we understand evil because we understand compassion, love and are capable of empathy whereas animals act on pure instinct. You can therefore not define evil or claim that something is evil if it does not have the capability of righteousness and goodness. Your language is very convuluted in places and sometimes thus also a bit difficult to follow see orange sentence.Do not use contractions. 12. ———————– [1] Stanza 1, line 1; â€Å"I sit in the top of the wood . . . â€Å" [2] Stanza 1, line 4;†Or in sleep rehearse perfect kills and eat† and stanza 3, line 2; â€Å"I kill where I please†. [3] Stan za 1, line 1; â€Å"I sit in the top of the wood† and stanza 4, line 2; â€Å"I kill where I please† [4] Stanza 4, line 2. [5] Stanza 3, line 2-3. [6] Stanza 1, line 2. [7] Stanza 4, line 3.

Addressing Challenges of Groups and Teams Essay

The use of teams in the workplace is continuing to grow because teams work more efficiently and are effective (Robbins & Judge, 2011). However with teams challenges and benefits present with group and team communication, collaboration, and conflict can arise. The Enron Corporation failed to have an effective plan to promote communication, collaboration, and address conflict. The following will review a plan that outlines the benefits and challenges of groups and team through the promotion of communication, collaboration, and address conflict. Creating an Effective Team  Three elements of an effective team are categorized as contextual, composition, and process (Robbins & Judge, 2011). The effectiveness of the team is dependent on the three elements collectively working together to form the team effectiveness. Contextual Factors The contextual factors determine the success of the team. The factors considered contextual are adequate resources, leadership and structure, climate of trust, and performance evaluation and reward system (Robbins & Judge, 2011). The adequate resources for a team begin with proper training about team development and how to work within a team. The team is supported by the organization and has the proper assistance to complete the tasks. The training plan for Enron begins with support from the organization. The team is supported by the executive leadership throughout the corporation. The failure of Enron resulted from the lack of executive leadership to support the ethical business practices within the organization. Therefore, an effective training plan with the support of the executive leadership is the key to success of ethical business practices throughout the organization. Leadership within a team is the key to the success of the team. See more:  Manifest Destiny essay Enron Corporation executive leadership failed to act as a leader and set the organizational objective for conducting business. The leader within the team helps the team define the shared objectives, member skills, and role clarity for the team members (Yukl, 2010). The leader of the team helps to establish the climate of trust among the members of the team. The climate of trust was not established throughout the Enron Corporation because the executive leadership knowingly engaged in accounting fraud and formation of illegal partnerships. The training plan allows each aspect of the contextual element to support the training plan for ethics throughout the organization. Composition Factors The composition factors of the effective team are composed of the abilities of the team members, personality of the members, and allocation of members. The team members have different skills and abilities identified and properly used to allow the member the reach the fullest potential as a member of the team. Identifying skills and abilities allows the proper allocation of roles (Robbins & Judge, 2011). Personality of members may have an effect on the team ability to complete tasks. Members of the team must be aware of their own personality to begin understanding how personality of others offers contributions to the team. Measuring emotional intelligence can help with self-reflection. â€Å"Emotional intelligence reflects the ability to read and understand others in social contexts, to detect nuances of emotional reactions, and to utilize such knowledge to influence others through emotional regulation and control† (Prati, Douglas, Ferris, Ammeter, & Buckley, 2003, p. 21). Therefore, leaders with high emotional intelligence assures self-reflection and reflection of others to determine the most appropriate way to interact with others. Team Processes The final element of effective teams is team processes. The team processes define the purpose and plan of the team. The processes set the goal for the team. Team efficacy occurs with continued success of the team. Team processes also provide plans for handling conflict as it occurs within the team. Applying the Training Program for Enron Enron’s collapse resulted from unethical business practices. The executive leadership within the corporation participated in the accounting fraud and hiding financial losses of the corporation. Enron’s code of ethics for the company should have served as a guide for employees ethically to conduct business practices. However, a waiver is included in the code of ethics that allowed the organization to engage in activities seen as a conflict of interest at the discretion of the chief executive officer (Elson & Gyves, 2003). The executive leadership failed to implement organizational behavior to instill ethical business practices throughout the company (Robbins & Judge, 2011). The initial step to applying the training plan is communication. Communication among the members of a team and a corporation serve as the first step toward success. Communication among the members of the team can occur through electronic mail, memos, and face-to-face meetings (Robbins & Judge, 2011). The leader of the team is responsible for communication between the team and the executive leadership. Communication serves to engage members of the organization, implement change, and establish a checks and balances systems. The Enron Corporation failed to communicate effectively throughout the organization. This lack of communication gave opportunity for the executive leadership to conduct unethical business practices. Collaboration among the members of an organization and team build the cohesiveness of the team and stimulate creativity to solve problems. Using collaboration to build the cohesion of the team keeps each team committed to the goals and mission of the organization. Collaboration will also help to maintain ethical business practices by assuring members of the organization responsible for the accounting and business practices are using checks and balances to report information accurately. Conflict is expected to arise in team and group work. Therefore, the leader must be dedicated to addressing conflict and guiding the team through the conflict. Failure to address conflict can lead to failure of the team (Robbins & Judge, 2011). The leader of the team will use the conflict process to work through conflict. The training plan for Enron that included managing conflict can help to address unethical business practices prior to occurrence. Through the use of internal and external audits deficiencies and conflicts can be identified and addressed before unethical business practices are implemented. Conclusion Communication, collaboration, and conflict management are keys to the success of teams and businesses. Enron failed to communicate, collaborate, and management conflict leading to the failure of a corporation. Enron allowed executive leaders to stifle communication, collaboration, and conflict management to hide fraudulent accounting practices. The implementation of a training plan supportive of communication, collaboration, and conflict management may have identified and addressed issues leading to the success rather than the failure of Enron Corporation.

Business Impact Of Business On Business - 858 Words

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