Answer
a. $\theta=60^{\circ}$
b. $\theta\approx 72^{\circ}$
c. $\theta\approx 84^{\circ}$
Work Step by Step
Let the intensity of the light after the first polarizer be $I_1$.
Use equation 24–5 to relate the final intensity to $I_1$.
$$I_2=I_1cos^2\theta $$
$$\theta=cos^{-1}\sqrt{\frac{I_2}{I_1}}$$
a. $\theta=cos^{-1}\sqrt{\frac{1}{4}}= 60^{\circ}$
b. $\theta=cos^{-1}\sqrt{\frac{1}{10}}\approx 72^{\circ}$
c. $\theta=cos^{-1}\sqrt{\frac{1}{100}}\approx 84^{\circ}$
