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. P
• B. Q
• C. R
  (D) S
• D.

Hint:

When thinking about shadows from parallel light, imagine looking at the object from the direction of the light source. The shadow is simply the object's 2D outline from that viewpoint. A circle, rectangle, and oval (ellipse) are all possible outlines of a cylinder, but a parallelogram is not.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question tests spatial reasoning and understanding of orthographic projections. We need to determine the possible 2D shapes (shadows) that can be created by projecting a 3D cylinder onto a plane using a parallel light source.
Step 3: Detailed Explanation:
The light beam is parallel, meaning the shadow is a direct projection of the cylinder's outline as seen from the light source's direction. The screen is perpendicular to the beam. Let's analyze the possible orientations of the cylinder relative to the light beam.
- Shadow P (Circle): This shadow is possible. If the cylinder is oriented such that its circular base is facing the light source directly (i.e., the axis of the cylinder is parallel to the light beams), the shadow cast will be a circle.
- Shadow R (Rectangle): This shadow is possible. If the cylinder is oriented such that its axis is perpendicular to the light beams (i.e., you are looking at the side of the cylinder), the shadow cast will be a rectangle. The length of the rectangle will be the length of the cylinder, and the width will be its diameter.
- Shadow Q (Oval/Ellipse): This shadow is possible. An ellipse is the projection of a circle viewed at an angle. If the cylinder is tilted so that its axis is neither parallel nor perpendicular to the light beams, the circular base will project as an ellipse. The overall shadow can take various forms, including an ellipse if viewed from a specific angle relative to its length and diameter. More generally, tilting the cylinder from the position that creates shadow R will result in the rectangular part remaining a rectangle, but the circular ends becoming visible as ellipses, creating a "stadium" or "obround" shape. However, a pure ellipse can also be a valid projection under certain tilt conditions. For the purpose of this question, an oval shape is a very plausible shadow.
- Shadow S (Parallelogram): This shadow is NOT possible. A cylinder is composed of two flat circular bases and a curved rectangular side. When projected by a parallel light source onto a perpendicular screen, straight lines project as straight lines and circles project as circles or ellipses. The sides of the cylinder are parallel to its axis. Their shadow will form parallel lines, resulting in a rectangle. The circular ends project as circles or ellipses. There is no orientation that will cause the rectangular profile to skew into a parallelogram. A parallelogram shadow would require a sheer transformation, which does not happen with this type of projection.
Step 4: Final Answer:
The shadow that is not possible to create is the parallelogram (S).
Step 5: Why This is Correct:
The projection of a cylinder by a parallel light beam onto a perpendicular screen can only produce shapes with either perpendicular sides (like a rectangle) or curved boundaries (like a circle or ellipse). A parallelogram has slanted, non-perpendicular sides, which cannot be formed from the silhouette of a right cylinder.