A printed transparent sticker (as shown on the left) is applied onto a glass cylinder such that the vertical edges meet. Which option is the correct representation?
Show Hint
When dealing with transparent objects, remember to distinguish between the front surface and the back surface. Patterns on the back surface will be visible but will appear distorted by the curvature of the object.
Step 1: Understanding the Concept:
This problem requires visualizing how a 2D pattern on a flat sticker appears when wrapped around a 3D transparent object (a cylinder). We must consider both the wrapping transformation and the effect of transparency, which allows us to see the pattern on the back surface.
Step 2: Key Formula or Approach:
1. **Analyze the sticker pattern:** Note the shapes (blue triangle, black lines) and their positions relative to the edges.
2. **Simulate the wrap:** The left and right edges will meet. The pattern on the left will be on the front-facing surface, while the pattern from the top-left will wrap around to the back.
3. **Account for transparency and curvature:** We will see the pattern on the back of the cylinder through its front. Lines on the curved back surface will appear curved to the viewer. Straight lines on the front surface will also appear curved unless they are perfectly vertical or horizontal at the point directly facing the viewer.
Step 3: Detailed Explanation:
Let's trace the key features of the sticker onto the cylinder:
The Blue Triangle: It occupies the left half of the sticker. When wrapped, it will be visible on the front-left side of the cylinder.
The Main Diagonal Line: The hypotenuse of the blue triangle runs from the middle of the left edge to the top of the central vertical line. This line will be on the front surface of the cylinder.
The Top-Left Line: The line segment from the top-left corner of the sticker will be on the back of the cylinder after wrapping. Because the cylinder is transparent, we will see this line through the glass. Due to the curvature of the back surface, this straight line will appear as a curve.
The Horizontal Line: This line segment will wrap around the front of the cylinder.
Now let's evaluate the options based on this analysis:
(A) This option correctly places the blue triangle on the front-left. The black lines on the front are correctly depicted. Crucially, it shows the line from the back (originating from the sticker's top-left) as a curved line visible through the cylinder. This representation is consistent with our analysis.
(B) The blue triangle is on the wrong side (right side). Incorrect.
(C) The main diagonal line on the front is shown with an incorrect curvature. A straight line on the cylindrical surface would not appear to curve down like that from this viewpoint.
(D) The pattern is heavily distorted in a way that doesn't match the simple wrapping of the sticker.
Step 4: Final Answer:
Option (A) provides the only physically correct representation of the sticker wrapped around the transparent cylinder.
