Unformatted text preview: dots ( in mode space ) and dV = 4 r 2 dr . Thus, dr r dr r dV r dr r N 2 2 1 2 8 1 4 ) ( ) ( ) ( = = = and df c L c Lf dr r dr r N df f N ) / 2 ( ) / 2 ( 4 ) ( ) ( ) ( 2 2 1 2 8 1 = = = , where I used r = (2L/c)f and dr = (2L/c)df and where the 1/8 comes from including only the positive integers. Hence, df c Vf df c Vf df f N 3 2 2 3 2 8 2 8 ) ( = yaxis zaxis xaxis O L L L n x n y n z Mode Space r Dot at every positive integer ( i.e. =1) corresponds to an allowed frequency! Must multiply by two for the two polarization state of light! Can show that N(f)df is independent of the shape and depends only on the volume V!...
View
Full Document
 Spring '07
 Field
 Physics, Radiation, Wavelength, Natural number, Conducting Cavity

Click to edit the document details