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Polarisation

Malu's Law

Light from the polarizer is incident on the analyzer

  • \(I = I_0\cos^2{\theta_i}\) , \(I_0\) is the initial intensity; \(\theta_i\) is the angle between the plane of the polarizer and the analyzer.
  • For a beam of unpolarized light, it contains light from all angles, so the value of \(\cos^2{\theta}\) can be thought of as the average, which is \(1/2\)

Hence, \(I/I_0 = 1/2\)

Proof of Malu's Law

  • \(I = A^2\) , \(I\) is the intensity, \(A\) is the amplitude
  • The electric vector of a light has an amplitude of \(E_0\). This can be decomposed into \(E_0\cos{\theta}\) and \(E_0\sin{\theta}\), \(\theta\) being the angle between the direction of oscillation of the light wave and the plane of the polarizer
  • The polarizer lets in the \(E_0\cos{\theta}\) component and absorbs the \(E_0\sin{\theta}\) component.
  • \(I_0 = (E_0\cos{\theta})^2\)
  • \(I/I_0 = (E_0\cos{\theta})^2/E_0^2=\cos^2{\theta}\)
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