27.8 Exercise 16

Prove that, if $I$ is the intensity of light transmitted by two polarizing filters with axes at an angle $\theta$ and $I '$ is the intensity when the axes are at an angle $\text{90}.\text{0}º - θ,$ then $I + I ' = I_{0,}$ the original intensity. (Hint: Use the trigonometric identities $\text{cos} \left(\right. 90.0º - \theta \left.\right) = \text{sin} \theta$ and $\text{cos}^{2} \theta + \text{sin}^{2} \theta = 1.$)