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?
Show Hint
For 3D solids, think about their cross-sections and projections: cylinders give circular, rectangular, or elliptical projections, but never skewed parallelograms.
Step 1: Recall geometry of a cylinder.
A cylinder can cast different types of shadows depending on how it is oriented relative to the light beam:
- If light falls along the axis of the cylinder, the shadow is a circle (like option P).
- If light falls perpendicular to the axis, the shadow is a rectangle (like option R).
- If light falls at an angle, the shadow can be an ellipse (like option Q).
Step 2: Consider option S.
Option S shows a parallelogram-shaped shadow. For a cylinder, whose cross-sections are circles and projections are always circular or rectangular (or elliptical combinations), it is impossible to produce a parallelogram-shaped shadow.
Step 3: Eliminate possibilities.
- P (circle) → possible.
- Q (ellipse) → possible.
- R (rectangle) → possible.
- S (parallelogram) → not possible.
