Question

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?

• A. \textbf{P}
• B. \textbf{Q}
• C. \textbf{R}
• D. \textbf{S}

Hint:

For silhouettes under parallel light, think “orthographic views.” A circular cylinder yields (i) circle (view along axis), (ii) rectangle (view sideways), or (iii) rounded rectangle with curved ends (oblique). A pure parallelogram cannot arise from a circular cylinder.

Answer 1

The Correct Option is D

Step 1: Translate the setup into geometry of orthographic projection.
A parallel light beam with a screen perpendicular to the beam produces a {parallel/orthographic projection} (no perspective). The silhouette of a right circular cylinder under orthographic projection depends on the angle between the viewing direction (the beam) and the cylinder axis.
Step 2: Enumerate possible silhouettes of a cylinder.
\begin{itemize}
View along the axis (beam parallel to axis): the circular end face is seen $\Rightarrow$ a circle (matches option P).
View perpendicular to the axis (beam orthogonal to axis): the generatrices project to two parallel straight edges; the end faces project to lines $\Rightarrow$ a rectangle (matches option R).
View at an oblique angle: the side generatrices still give two parallel straight edges, while the end faces project to {elliptic} arcs, producing a rounded-rectangle (“stadium”) silhouette (matches option Q). \end{itemize}
Step 3: Test the remaining option.
Option S is a {parallelogram} with four straight edges, including two {slanted} non-parallel edges. A cylinder’s orthographic silhouette can contribute only: \begin{itemize}
straight edges from side generatrices (always a {pair of parallel} lines), and
curved edges from the ends (circles/ellipses), never straight slanted edges. \end{itemize} Hence forming a parallelogram with four straight edges is impossible for a circular cylinder. Final Answer: \[ \boxed{S} \]