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METR 415/715

METR 415/715. Monday February 11 2013. Reading Assignment – Chapter 6 of Petty text. Homework #1 Due Today. Will accept it with no penalty if you hand it in at start of Wednesday. I’m prepared to discuss “hints” today Make sure I thatyour answer contains the following: What’s given – 10%

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METR 415/715

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  1. METR 415/715 Monday February 112013

  2. Reading Assignment – Chapter 6 of Petty text

  3. Homework #1 Due Today • Will accept it with no penalty if you hand it in at start of Wednesday. • I’m prepared to discuss “hints” today • Make sure I thatyour answer contains the following: • What’s given – 10% • What you need to find out – 10% • Physical relation(s) involved - 20% • Solve for the unknown on LHS of equation – 20% • Check that the answer comes out in the right units—20% • Plug in numerical values and state the answer – 20% • If possible, check whether solution is reasonable

  4. Other items about the HW – Part 1 • Not every problem will follow this procedure exactly, but most will. • Some might ask you to explain something in words • Some might require a brief presentation to the class that might involve discussing the content of a web page • Finally, none of us like tedium. No need to repeat the procedure, especially for a multi-part problem, exactly when it is clear to me that you have followed the problem solving procedure clearly

  5. Other items about the HW – Part 2 • Every HW problem will be given a value of 10 points • At this point I don’t know the total number of homework problems that I will assign during the semester • Starting with next HW problem set I will deduct 2 points for late submission • If you delay turning in your problem set for more than a week after it is due, you will get no credit for it • I plan to return your graded homework, with a full discussion of the answers, a week after you hand it in.

  6. REVIEW FROM LAST WEEK • FROM CHAPTER 2: • SOLID ANGLES AND STERADIANS • FROM CHAPTER 4: • SPECULAR REFLECTION • ABSORPTION • REAL AND IMAGINARY PART OF INDEX OF REFRACTION • SNELL’S LAW • BEER’S LAW

  7. Beer’s Law • The intensity of a beam of monochromatic radiation falls off exponentially as it traverses a uniform medium • The rate at which it falls off is proportional to βa

  8. Intensity as a function of travel through a medium • Eq 4.2, p.77 • Βa= absorption coefficient

  9. Intensity as a function of travel through a medium • Eq 4.3, p.77

  10. Penetration Depth • Defined as the value of x for which t(x) = e-1 or approximately 37% • Check Figure 4.2 on page 79 for water and ice • How does that influence color of pools water? Light penetration into the ocean?

  11. TODAY’S AGENDA • Solid angle demonstration • Absorptivity and reflectivity • Defined as the fraction of the intensity of an incident beam of radiation that is absorbed or reflected • They can be a function of the angle of incidence of the ray, of the nature of the interface between the two media, and of the complex indices of refraction • They add up to 1 • Black bodies • Planck’s Function – Wien’s Law and Stefan-Boltzmann’s Law

  12. Specular vs. Lambertian Reflection • Decription and illustration in Chapter 5

  13. Definition of a black body • Perfect absorber of radiation • Absorptivity = 1.0 • Figure 6.1 p.116 • Perfect absorbers of radiation are also perfect emitters of radiation • Absorptivity = Emissivity (Kirchhoff’s Law) • Equation 6.12 p.126

  14. Planck’s Function • Refers to the radiation that a blackbody emits in every direction in a huge range of wavelengths • Equation 6.1 describes Planck’s Function • Planck’s Function applies to BLACK BODIES (PERFECT EMITTERS OF RADIATION) and varies with wavelengh and temperature

  15. Wien’s Law • Defines the wavelength of the maximim value of Planck’s function • First derivative of Planck’s function set = 0

  16. Stefan- Boltzman Law • Integral of Planck’s function over all wavelengths

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