Polarization question?

Question

A beam of plane-polarized microwaves is incident upon an aerial which is positioned to give maximum response. The aerial is rotated at an angle of 30 degrees to the plane of polarization about the direction of the incident waves.
Calculate the % reduction in the amplitude of the signal now received from the aerial.

Answer 1

The signal strength goes as (cos(theta))^2, where theta is the angle of mis-alignment between the two devices.

When they are aligned, you have
(cos(0))^2
= 1^2
= 1

When they are 30 degrees misaligned, you have
(cos(30 deg))^2
= (sqrt(3)/2)^2
= 3/4

So, the signal strength will be at 3/4 of its ideal value when it is 30 degrees misaligned, a 25% loss in signal strength.