That's an excellent and practical question that touches on urban design, public health, and social responsibility. There isn't a single universal depth measurement, as effectiveness relies more on integrated design principles than on a specific centimeter count. The primary goal is to make retrieving items physically difficult and unrewarding.
The most effective strategy is using bins with narrow openings or specialized lids (like swinging flaps or small circular holes) that limit arm access. A bin can be quite deep, but if the opening is wide, it's still easily accessible. Therefore, depth should be combined with restricted aperture. A good rule of thumb is that the opening should be positioned so that even with a fully extended arm, a person cannot reach the bottom. For a standard cylindrical bin, this often means a depth of at least 100-120 cm (about 3-4 feet) from the opening.
More crucial than extreme depth is the use of secure, lidded containers that are regularly emptied. Overflowing bins are a major incentive for scavenging. Modern solutions include compacting bins that crush waste, making it inaccessible, and bins with locked inner liners.
Ultimately, the best "depth" is a holistic design depth that considers the opening, the mechanism, and maintenance frequency. It's about creating a system where the effort to dig through trash significantly outweighs any perceived reward, thereby protecting public health and dignity.