## Conceptual Physics (12th Edition)

Call the Polaroids 1, 2, and 3, in the order in which light encounters them. Say that filter #1 has a vertical polarization axis and #3 has a horizontal one. Filter #1 polarizes the incoming unpolarized light, letting half of it through, which now has a vertical polarization direction. This direction is perpendicular to the axis of filter #3. When these are the only filters present, no light gets through. However, when filter #2 is placed between 1 and 3, oriented diagonally, it is illuminated by polarized light that is aligned at $45^{\circ}$ to its own axis. It lets half of the light through, and polarizes it with a diagonal direction of polarization. The light illuminating filter #3 is now also aligned at $45^{\circ}$ to its own axis. So filter #3 also transmits half of the light that strikes it, which is one-eighth the intensity of the initially unpolarized light that illuminated filter #1. For more on this, look up the "Law of Malus" for polarizing filters. This is discussed on pages 555-556, and an analogy with ropes passing through a pair of picket fences is shown in Figure 29.32. This problem is discussed in the caption to Figure 29.34 and the answer is in Appendix D.