Polarization — Question 10

Question 10

Removing a polarizer can reduce the light reaching a fixed final axis

An x-polarized beam of intensity I0 encounters ideal polarizers at 30 degrees, 60 degrees, and 90 degrees, in that order. The initial polarization and final axis remain fixed.

1. Find the final transmission with all three polarizers and with the middle 60-degree element removed.

2. Find the transmission after swapping the 30-degree and 60-degree elements, and quantify the order dependence.

Question 10 - Solution

Removing a polarizer can reduce the light reaching a fixed final axis

(a) Method and calculation

$$I_{30,60,90}=I_0(\cos^230^\circ)^3=\boxed{27I_0/64}.$$$$I_{30,90}=I_0\cos^230^\circ\cos^260^\circ=\boxed{3I_0/16}.$$

(b) Interpretation and further calculation

$$I_{60,30,90}=I_0\cos^260^\circ\cos^230^\circ\cos^260^\circ=\boxed{3I_0/64}.$$$$\boxed{I_{30,60,90}/I_{60,30,90}=9}.$$

Physical check

Each transmission depends on the immediately preceding polarization, so changing the order changes the product of projections.