Answer
The ratio of the transmitted intensity to the incident intensity is $\frac{1}{16}$
Work Step by Step
We can write an expression for the incident intensity:
$I_1 = c~\epsilon_0~E_1^2$
We can write an expression for the transmitted intensity:
$I_2 = c~\epsilon_0~E_2^2$
$I_2 = c~\epsilon_0~(\frac{E_1}{4})^2$
$I_2 = \frac{1}{16}\times c~\epsilon_0~E_1^2$
$I_2 = \frac{1}{16}\times I_1$
The ratio of the transmitted intensity to the incident intensity is $\frac{1}{16}$
