<p>Exam 3 Review Chapters 9-11</p><p>Equations that will be given on the exam. All of the equations/constants from exam 2, plus the following:    Rays: R(r)  n(r)sˆ(r) A  D Cavity stability: 1 1 Single slit: FT= (1 2p ) a sinc( kx a 2) ABCD Matrices 2 Rectangle: 1 d  Diffraction formulas   2 2 Translation:   Helmholtz equation: � E(r ) k E ( r ) FT= (1 2p ) ab sinc( kx a 2) sinc( k y b 2) 0 1  Fresnel approximation: Top hat: 1 0 k 2 2 骣 i x2+ y 2 Flat surface refraction: 琪 ikz 2z ( ) FT= a J1 ( kr a) k r a = ajinc( k r a ) 0 n n ie e 桫 1 2 E( x , y , d ) = - lz xh  1 0 骣 k k Spectrometer:   ,   琪 i xⅱ2+ y 2 - i( xx ⅱ + yy ) mN 1 2z( ) z md Curved surface refr: 琪 n n-1 n n E( xⅱ , y ,0) e e dx ⅱ dy ( 1 2) 1 2 蝌 1.22 桫R aperture  min  R = + for convex, – for concave Fraunhofer approximation: l k Gaussian Beams 骣 1 0 i x2+ y 2 Spherical mirror/thin lens: ikz 2z ( ) 2 2 琪 ie e -r ikr 1骣 z 桫-1f 1 E( x , y , z ) = - ikz+ - i tan- 琪 w0 w2 2R桫 z0 -1 lz E( x, y , z) = E0 e e f=轾 n n -1 1 R - 1 R k lens 臌( 2 1)( 1 2 ) -i( xxⅱ + yy ) w z E( xⅱ , y ,0) e dx ⅱ dy 2 2 2 R = + for convex surface; – for 蝌 kw0 z 0 z aperture z=, R = z + , w = w 1 + concave surface 0 0 2 Fourier Transforms: 2 z z 0 R Aq+ B fmirror  , R = positive for concave Comb function (N total deltas): 1 2 q2=; q = z + iz 0 FT= 1 2p sin N w t 2 sin w t 2 Cq1 + D p1 = (1–D)/C, p2 = (1–A)/C, f = -1/C ( ) ( 0) ( 0 )</p><p>Equations that you won’t need to know by heart. (Or, if you do, I will give them in the problem statement.)  ABCD matrix for thick lens  Numerical aperture  “Fresnel’s diffraction formula”  “The Fresnel-Kirchhoff diffraction formula”  Bessel function formulas  Complicated formula for diffraction through a lens (Eqn 11.14)</p><p>Equations/derivations/other stuff that you may need to know by heart. All of the items listed for exam 2, plus the following (not an exhaustive list):  OPL= ndℓ  Fermat’s principle of least time  If ABCD matrix includes whole trip, then B = 0 is requirement for focusing, and A = magnification  Thin lens equations: 1/f = 1/p + 1/q; M = -q/p  Aberrations: names & effects  f-number, including how it relates to angle of light cone  Babinet’s principle 2  IFraunhofer = I0  |2DFT of aperture function| with kx = kx/z, ky = ky/z (z = distance to screen, x & y = coordinates on screen)  Convolution theorems (in context of diffraction)  2 slit diffraction formula (because 2 slit aperture function is just single slit  2 delta functions)  FT transform of function shifted from origin (because it’s just function at origin  shifted delta function)  Array theorem (because an array is just an aperture  a bunch of shifted delta functions)  Intensity from diffraction grating (because it’s a single slit  a comb function)</p><p>Exam 3 Review</p>