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.
• \(I_0 = (E_0\cos{\theta})^2\)
• \(I/I_0 = (E_0\cos{\theta})^2/E_0^2=\cos^2{\theta}\)