METR 415/715 Monday February

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% – 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

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

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.

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

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 β a

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

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

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?

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

Specular vs. Lambertian Reflection Decription and illustration in Chapter 5

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

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

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

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