Announcements Exam 3 starts Thur noon, and continues through Mon close, in the Testing Center. It will include both conceptual questions and homework style problems. Ch 9-11 Formulas for Ex 3 are posted online.

Physically, what does the Eikonal Equation represent and how do you use it? Can we have an example of how to use the OPL equation with Fermat's principle? In ABCD laser cavity matrices, is it possible to find the focus and how would you do that ? –see Appendix 11.A, which we haven’t studied. For a ray starting and ending in the same medium, what condition in the ABCD matrix is s step toward solving for the relation between the effective focal length and the image and object distances? Describe the spherical aberration Describe how astigmatic aberrations occur. Chapter 9

9.15? Can you just show how we'd set it up? 3 image-object pairs In the context of the eikonal equation and surfaces of constant phase, can we go over how to find R(r) and Eo(r) for certain shapes of waves (spherical, cylindrical, etc.)? –Two principles: R(r) has the symmetry of the case, and I*area = constant (conserves power.) What approximations/assumptions involving lambda or k do we make when deriving the eikonal equation? Geometrically, where are the principle planes in a diagram of optical elements? …but what does this physically/conceptually mean? Do any of the lens aberrations we talked about in class appear in a specific way in the ABCD matrix of a lens? --No What are the underlying assumptions and ideas that derive Fermat's Principle from the Eikonal Equation? –I don’t go into this. We talked in class about how two rays going through a lens though having different geometrical path lengths can have equal path lengths because one ray goes through more material. Can you please explain this? Chapter 9

Can we see some more visuals of light diffracting through common apertures (rectangular, circular, etc) with increasing z to see the switch between the Fresnel and Fraunhofer approximations? Example from class: A laser beam has a Gaussian profile of 2mm width, and a constant phase across the beam. How wide will it be after propagating 100m? Could we go over some examples of fraunhofer intensity patterns for different shapes of apertures? Under what conditions do you use the fresnel and fraunhofer approximations? Chapter 10 Is there a more precise point when we should switch from Fresnel to Fraunhofer? Can we go through why the Fresnel regime switches to Fraunhofer when z>>(k/2)*(aperture radius)^2?

We've done alot with fraunhoffer diffraction but not so much with Fresnel, What are some examples of things we can do with Fresnel? Can we go over a diffraction example with Cylindrical Symmetry? What difference does a cylindrically symmetrical aperture make (and look like -> Graphically)? How can we differentiate this from other apertures? Which derivations from the diffraction integral should we be familiar with? Which equation for far field should we know: equation in the book, one the one from lecture? If I block zones 2 and 3 and keep zones 1 and 4 open, what would I get? Chapter 10

How can we define the resolving power of the diffraction grating? Is the angular width of the pattern is preserved in Fraunhofer diffraction? Is there an uncertainty relationship that tells us that as N increases for diffraction grating that the peaks should be more narrow or there should be more intermediate peaks? How do you do problem 11.5? Is there a way to intuit what the pattern will be with an array of apertures before using the entire array theorem? Can you go over the gaussian laser beams and understanding beam waist How does the monochromator and spectrometer work? Chapter 11

How do you do problem 23x (c)?

How do you calculate the beam waist of a laser in a cavity with 2 mirrors like the homework problem? Could we do an example using the array theorem from section 11.3? If I block zones 2 and 3 and keep zones 1 and 4 open, what would I get? How would you make a zone plate that only allows through odd numbered zones? Why does the on-axis intensity behind a circular aperture fluctuate, while the on-axis intensity behind a circular block doesn't? (Is there some way to see this conceptually instead of mathematically?) Chapter 11