Question 24.8: Polarizer GOAL Understand how polarizing materials affect li...
Polarizer
GOAL Understand how polarizing materials affect light intensity.
PROBLEM Unpolarized light is incident upon three polarizers. The first polarizer has a vertical transmission axis, the second has a transmission axis rotated 30.0° with respect to the first, and the third has a transmission axis rotated 75.0° relative to the first. If the initial light intensity of the beam is I_{b} , calculate the light intensity after the beam passes through (a) the second polarizer and (b) the third polarizer.
STRATEGY After the beam passes through the first polarizer, it is polarized and its intensity is cut in half. Malus’s law can then be applied to the second and third polarizers. The angle used in Malus’s law must be relative to the immediately preceding transmission axis.
(a) Calculate the intensity of the beam after it passes through the second polarizer.
The incident intensity is I_{b}/2. Apply Malus’s law to the second polarizer:
I_{2}=I_{0}\cos^{2}\theta=\frac{I_{b}}{2}\cos^{2}(30.0^{\circ})=\frac{I_{b}}{2}\biggl(\frac{\sqrt{3}}{2}\biggr)^{2}={\frac{3}{8}}I_{b}
(b) Calculate the intensity of the beam after it passes through the third polarizer.
The incident intensity is now 3I_{b}/8. Apply Malus’s law to the third polarizer.
I_{3}=I_{2}\mathrm{cos}^{2}\,\theta=\frac{3}{8}I_{b}\mathrm{cos}^{2}\,(45.0^{\circ})\,=\frac{3}{8}I_{b}\bigg(\frac{\sqrt{2}}{2}\bigg)^{2}={\frac{3}{16}}I_{b}
REMARKS Notice that the angle used in part (b) was not 75.0°, but 75.0° – 30.0° = 45.0°. The angle is always with respect to the previous polarizer’s transmission axis because the polarizing material physically determines what direction the transmitted electric fields can have.