From: jos.bergervoet@xs4all.nl   
      
   On 2/5/2018 6:30 PM, questionsphysics13@gmail.com wrote:   
   > I understand that light from stars is coherent and can be treated   
   > as a plane wave. I wonder how can I calculate the amplitude A of   
   > such plane wave A exp[ct-kx] for a given star form its magnitude,   
   > bandwidth, distance and other parameters of the star.   
   >   
   > What is the typical range for A for a typical wavelength?   
   >   
   > Thanks   
   >   
   > [[Mod. note --   
   > 1. The light from a star is *incoherent* -- each of the huge number   
   >     of atoms in the star's photosphere is radiating independently, and   
   >     the light we receive is (that tiny fraction that happens to be   
   >     radiated in our direction) the incoherent sum of light from many   
   >     of those atoms.   
   > 2. The light from a star is coming from very far away, so to a *very*   
   >     good approximation it can be treated as a plane wave.   
   > 3. The amplitude of a plane wave is directly related to the intensity   
   >     of the light, i.e., how bright the star is.  The book "Astrophysical   
   >     Quantities", by Allen, has numbers for home many photons/second   
   >     per square centimeter of detector area we receive for a given   
   >     magnitude star, but I don't recall these offhand.  Converting to   
   >     an amplitude of a plane wave takes a little bit more algebra...   
   > -- jt]]   
   >   
      
   Sun, with magnitude of -27: irradiation = 1kW/m^2 (below atmosphere).   
      
   One magnitude step is 4 dB, is 10^0.4 times less power. Bright stars   
   have magnitude around 0, so 10^(-27*0.4) * 1000 W/m^2   
      
   This power density is E-field squared divided by wave impedance,   
   the latter is mu0*c ~= 367 Ohm. So E-field strengths: (approximately)   
      
      magnitude -27  ==>  600 V/m    (Sunlight)   
      magnitude   0  ==>  2.5 mV/m   (One star of top-5 of brightest stars)   
      magnitude   6  ==>  150 uV/m   (Weakest stars the eye can see)   
      
   Incidently, the signal from a radio station is also in the order   
   of 100 uV/m. (Of course sensitive receivers can detect much weaker   
   signals, just like big telescopes can see much fainter stars).   
      
   These are amplitudes of the total EM signal, all frequencies   
   (wavelengths) added together to one time-dependent E-field.   
      
   --   
   Jos   
      
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