(Solution) - Suppose that you held two polarizing sheets in front of -(2025 Original AI-Free Solution)

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Suppose that you held two polarizing sheets in front of you and looked through both of them. How many times would you see the sheets lighten and darken
(a) If one were rotated through one complete rotation,
(b) If both were rotated through one complete rotation at the same speed in opposite directions,
(c) If both were rotated through one complete rotation at the same speed in the same direction,
(d) If one were rotated twice as fast as the other and the slower one were rotated through one complete rotation?