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?
[The figure shows a solid circular cylinder and four shaded shadows: P a circle, Q a rectangle with semicircular ends, R a rectangle, and S a parallelogram with slanted ends.]
Answer: D
The impossible shadow is S, the parallelogram.
With a parallel beam and a screen perpendicular to it, the shadow is the orthographic projection of the cylinder. Looking along the axis gives a circle (P). Looking at right angles to the axis gives a rectangle (R). At any angle in between, the circular ends project as ellipses and the shadow is a band with rounded ends, the shape of Q.
A parallelogram would need the ends to project as straight, slanted lines. A circular end can only project as a circle, an ellipse or, edge-on, a straight line perpendicular to the sides, so slanted straight ends never occur.
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