Answer
(a) Plate (c) transmits the microwaves the best.
(b) Plate (a) reflects the microwaves the best.
(c) The intensity transmitted through the second-best transmitter is $\frac{I_1}{4}$
Work Step by Step
(a) Since the microwaves are polarized vertically, the microwaves would be transmitted best through slits that are lined up vertically. Therefore, plate (c) transmits the microwaves the best.
(b) Since the microwaves are polarized vertically, the microwaves would be reflected best through slits that are lined up horizontally. Therefore, plate (a) reflects the microwaves the best.
(c) Since the microwaves are polarized vertically, the angle $\theta$ between the polarization direction of the microwaves and the slits in plate (b) is $60^{\circ}$.
Let $I_0$ be the initial intensity. We can use Malus' law to find the transmitted intensity:
$I = I_0~cos^2~60^{\circ} = \frac{I_0}{4}$
Since the slits in plate (c) are lined up vertically, the transmitted intensity through plate (c) is $I_0$. Therefore $I_1 = I_0$.
The intensity transmitted through the second-best transmitter, which is plate (b), is $\frac{I_1}{4}$
