Answer
a) $\theta=48.03^{\circ}$
b) decrease
Work Step by Step
(a) We know that
$I_A=I_pcos^2\theta$
$\implies I_A=I_{\circ}cos^4\theta$
Bug given that $I_A=0.200I_{\circ}$
Thus $0.200I_{\circ}=I_{\circ}cos^4\theta$
$\implies cos^4\theta=0.200$
$cos\theta=(0.200)^{\frac{1}{4}}$
$\theta=cos^{-1}(0.200)^{\frac{1}{4}}$
$\theta=48.03^{\circ}$
(b) We know that the intensity and the angle $\theta$ are inversely proportional, thus if $\theta$ is increased then the transmitted intensity will decrease.
