When linearly polarized light passes through a polarizer, its polarizing axis may be rotated by any angle ϕ < 90° at the expense of a loss of intensity, as determined by Malus’s law. By using sequential polarizers, you can achieve a similar axis rotation but retain greater intensity. In fact, if you use many intermediate polarizers, the polarization axis can be rotated by 90° with virtually undiminished intensity. (a) Derive an equation for the resulting intensity if linearly polarized light passes through successive N polarizers, each with the polarizing axis rotated by an angle 90°/2N larger than the preceding polarizer. (b) By making a table of the resulting intensity for various values of N, estimate the minimum number N of polarizers needed so that the light will have its polarization axis rotated by 90° while maintaining more than 90% of its intensity. (c) Estimate the minimum number of polarizers needed to maintain more than 95% and 99% intensity.

When linearly polarized light passes through a polarizer, its polarizing axis may be rotated by any angle ϕ < 90° at the expense of a loss of intensity, as determined by Malus’s law. By using sequential polarizers, you can achieve a similar axis rotation but retain greater intensity. In fact, if you use many intermediate polarizers, the polarization axis can be rotated by 90° with virtually undiminished intensity. (a) Derive an equation for the resulting intensity if linearly polarized light passes through successive N polarizers, each with the polarizing axis rotated by an angle 90°/2N larger than the preceding polarizer. (b) By making a table of the resulting intensity for various values of N, estimate the minimum number N of polarizers needed so that the light will have its polarization axis rotated by 90° while maintaining more than 90% of its intensity. (c) Estimate the minimum number of polarizers needed to maintain more than 95% and 99% intensity.