A hollow cylinder is lit by sunlight at 45 degrees as shown on the left. If seen from a fixed point, which option is the closest representation of the lit area inside the cylinder?
Show Hint
Projecting a circle onto a concentric cylindrical surface always yields smooth, continuous curved boundaries. Avoid options with sharp, angular corners on the cylinder walls.
Step 1: Understanding the Question:
This question belongs to the topic of
Light, Shadow Casting, and Descriptive Geometry.
A vertical hollow cylinder is illuminated by parallel rays of sunlight coming from the top-left at an angle of 45 degrees. We must identify the correct visual representation of the lit area cast onto the interior wall of the cylinder.
Step 2: Key Formula or Approach:
We model the light projection geometrically:
• The top rim of the cylinder is a horizontal circle.
• Parallel light rays passing through this circle project it along a 45-degree vector onto the interior cylindrical wall.
• The intersection of a tilted circular cylinder of light with a vertical cylinder forms a curved boundary that appears as a smooth, sweeping crescent on the opposite inner wall.
Step 3: Detailed Explanation:
• Let us analyze the shape of the lit patch:
- The light enters from the top-left, so the shadow is cast on the left interior wall, leaving the right interior wall illuminated.
- Because the cylinder is curved, the transition of the shadow edge is a smooth, continuous curve.
- In Option (A), the lit region is a smooth, elegant crescent shape on the right side that tapers naturally towards the bottom. This is the mathematically correct projection of a circle onto a cylinder at 45 degrees.
- Option (B) shows a sharp angular break at the top, which is geometrically incorrect.
- Option (C) and (D) show distorted profiles that do not match the physics of parallel light rays.
Step 4: Final Answer:
Option (A) is the closest and most accurate representation of the lit area.
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