Problem 5.158

A plane monochromatic wave of natural light with intensity \(I_{0}\) falls normally on an opaque screen with round hole corresponding to the first Fresnel zone for the observation point \(P .\) Find the intensity of light at the point \(P\) after the hole was covered with two identical Polaroids whose principal directions are mutually perpendicular and the boundary between them passes (a) along the diameter of the hole; (b) along the circumference of the circle limiting the first half of the Fresnel zone.