Polarization — Question 5

Question 5

A finite extinction ratio leaves residual light through a crossed pair

Two identical imperfect linear polarizers transmit intensity fractions a=0.90 and b=0.01 along their principal and perpendicular axes, with no mixing. Unpolarized intensity I0 enters the pair.

1. Find the intensity and degree of linear polarization after the first element.

2. Find the final intensity for parallel and crossed axes and their ratio.

Question 5 - Solution

A finite extinction ratio leaves residual light through a crossed pair

(a) Method and calculation

$$I_1=I_0(a+b)/2=\boxed{0.455I_0}.$$$$\boxed{\mathcal P_L=(a-b)/(a+b)=89/91=0.97802}.$$

(b) Interpretation and further calculation

$$\boxed{I_{\parallel}=I_0(a^2+b^2)/2=0.40505I_0,\quad I_{\perp}=I_0ab=0.009I_0}.$$$$\boxed{I_{\parallel}/I_{\perp}=(a^2+b^2)/(2ab)=45.0056}.$$

Physical check

The two incoherent orthogonal components must be tracked separately through both elements.