Question

Below is an image of a reflective Steel Tumbler kept on a table cloth with a grid pattern. 
Task: 
Draw the pattern as reflected on the steel tumbler in the space/image provided below.

Hint: Consider how straight lines appear curved when reflected on a cylindrical surface. Pay attention to distortion, compression, and curvature of the grid.

Hint:

When drawing a grid pattern reflected on a curved surface like a steel tumbler, remember the lines will appear curved, not straight. Vertical lines will bend inward (like an hourglass shape), and horizontal lines may curve upward or downward depending on the tumbler’s shape. The reflection compresses and distorts the grid—think of it like wrapping the grid around a cylinder. Keep the center lines more vertical and bend the outer lines more dramatically to show curvature.

Answer 1

Reasoning
The reflection of the grid pattern on the steel tumbler is a classic example of reflection on a convex cylindrical surface. The specific distortion is determined by the shape of the tumbler and the principles of geometric optics.
1. The Reflecting Surface
Shape: The tumbler is a right circular cylinder. Its highly polished steel surface acts as a convex mirror.
Convex Reflection: A convex mirror diverges light rays and always produces a virtual, upright, and diminished image. For a cylindrical shape, the degree of magnification or diminution changes depending on the angle of incidence.
2. Distortion of Horizontal Lines (Lines Parallel to the Base) 
The horizontal lines of the tablecloth grid (lines parallel to the floor) appear as concave curves that bow inward toward the center of the tumbler's visible surface. 
Principle: Light rays from parts of the tablecloth farthest from the center of the tumbler (i.e., the edges of the visible area) are reflected more steeply due to the curvature. 
Effect: This “squeezes” the horizontal lines together and makes them bend inward, creating a pinched effect at the center. The lines appear closer together near the middle than at the sides. 
3. Distortion of Vertical Lines (Lines Perpendicular to the Base) 
The vertical lines of the grid appear as convex curves or remain relatively straight but fanned outward slightly. 
Principle: Because the tumbler has straight vertical sides, light rays from vertical lines are reflected with minimal vertical distortion. 
Effect: As the grid lines move from the center outward, they are slightly compressed horizontally but maintain a vertical orientation. They appear to radiate gently from a central vertical axis. 
4. The Combined Pattern (The "Warped Grid") 
The horizontal lines transform into steeply curved, concave arcs. 
The vertical lines remain mostly straight but subtly curved to intersect the horizontal arcs at near right angles, in accordance with reflection laws. 
Conclusion
This combination creates the visual effect of a warped, spiderweb-like mesh draped over the cylindrical surface. The distortion is a result of convex reflection and accurately follows principles of geometric optics, matching what is depicted in the image.