**Core Concept**
The question tests the understanding of radiographic positioning in dental restorations, specifically for observing recurrent caries under a class II amalgam restoration. Vertical angulation is crucial in dental radiography to obtain accurate images and diagnose potential issues like recurrent caries.

**Why the Correct Answer is Right**
To observe recurrent caries under a class II amalgam restoration, the vertical angulation of the central X-ray beam should be parallel to the buccolingual plane of the gingival surface of the restoration. This positioning allows for a clear view of the interproximal areas, where recurrent caries often occur. By angulating the beam in this manner, dentists can effectively diagnose and treat these issues before they become more severe. The buccolingual plane of the gingival surface of the restoration serves as a reference point for this positioning, ensuring accurate and informative radiographs.

**Why Each Wrong Option is Incorrect**
**Option A:** Perpendicular to the film placed is incorrect because it does not account for the specific needs of observing recurrent caries under a class II amalgam restoration. This positioning may not provide a clear view of the interproximal areas.

**Option B:** Perpendicular to the occlusal surface of the tooth is incorrect because it would not provide an adequate view of the interproximal areas, where recurrent caries often occur.

**Option D:** Perpendicular to the cavosurface bevels in the proximal box is incorrect because this positioning may lead to overlapping of the restoration margins and the interproximal areas, making it difficult to diagnose recurrent caries.

**Clinical Pearl / High-Yield Fact**
When taking radiographs of dental restorations, it's essential to remember that the vertical angulation of the X-ray beam can significantly impact the diagnostic accuracy. Always consider the specific needs of the case, such as observing recurrent caries under a class II amalgam restoration, and adjust the beam angulation accordingly.

**✓ Correct Answer: C. Parallel to the buccolingual plane of gingival surface of restoration**