Answer
a. $\theta\approx 35^{\circ}$
b. $\theta\approx 63^{\circ}$
Work Step by Step
Let the initial intensity be $I_o$.
The initial light is unpolarized, so the intensity after the first polarizer, $I_1$, will be half the initial intensity.
Use equation 24–5 to relate the final intensity to $I_1$.
$$I_1=\frac{1}{2}I_o$$
$$I_2=I_1cos^2\theta=\frac{1}{2}I_o cos^2\theta $$
$$\theta=cos^{-1}\sqrt{2\frac{I_2}{I_o}}$$
a. $\theta=cos^{-1}\sqrt{2\frac{1}{3}}\approx 35^{\circ}$
b. $\theta=cos^{-1}\sqrt{2\frac{1}{10}}\approx 63^{\circ}$
