Discussion
An opaque cylinder (shown below) is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The cylinder can be reoriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT possible?
Answer: D
The impossible shadow is S, the parallelogram.
With parallel light falling square on the screen, the shadow is the orthogonal projection of the cylinder. Looking along its axis gives a circle (P). Looking side-on gives a rectangle (R). At any angle between, the two circular ends project as ellipses joined by straight tangent lines, giving a rounded shape like Q.
A parallelogram would need slanted straight ends, but the ends of a cylinder are circles, and a circle projects as a circle, an ellipse or, edge-on, a straight segment perpendicular to the axis's projection. Edge-on ends give the rectangle R, never slanted sides, so S cannot occur.
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