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Why the Sky is blue? | A mathematical analysis

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Whenever a visible light with electric field E= E_o \cos \omegat strikes the Oxygen or Nitrogen atom, the electron revolving around the nucleus gets accelarated with an accelaration a. There will be two forces acting on an electron orbiting the nucleus. Firstly, there is an external forceĀ F_E=qE(Basic definition) . When this force acts on an electron, the electron starts to accelarate. At that time, there will be a restoring forceĀ F_R=-Kx where K=(Constant defined by an atom).

Mathematically K can be defined as \omega_o^2=\frac {K} {m}

Applying Newton’s second law of motion to the accelarating charge(Oxygen or Nitrogen atom).

F_N= F_E + F_R=ma where m=mass of an electron and a=accelaration.

D^2x*m=-Kx+F_E

Divide both L.H.S and R.H.S by m.

D^2x= –\omega_o^2 x+\frac {q*E_o}{m} \cos \omegat

 

D^2x + (more…)

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