That's an excellent and practical question that touches on urban design, public health, and behavioral psychology. From my experience observing and researching public spaces, there isn't a single universal "magic number" for depth, but rather a set of effective design principles where depth is a key factor.
The primary goal is to make retrieving items from the bin physically inconvenient and visually unappealing. A bin that is simply deep isn't enough; it needs to work in concert with other features. A depth of around 30 to 36 inches (roughly 75 to 90 cm) is often considered a effective starting point for standard public bins. This is deep enough that an average person cannot easily see the bottom or reach in without significant effort, especially when combined with a narrow opening.
However, depth alone is easily defeated. The most critical companion to depth is a secure, well-designed lid. An opening just large enough for trash disposal—often a slot or a small circular opening—prevents easy arm access and visual scanning of the contents. This makes "digging" a blind, difficult, and messy process. Motion-sensor or pedal-operated lids add another layer of inconvenience.
The material and placement matter too. Opaque materials (not clear plastic) hide the contents. Placing bins in well-lit, high-traffic areas increases social deterrence. For high-security areas, some designs incorporate internal baffles or mechanisms that make contents fall into a lower, inaccessible compartment.
Ultimately, the ideal "deep" bin is one that successfully shifts the cost-benefit analysis for a potential scavenger. By making the action difficult, time-consuming, and conspicuous, it encourages people to move along. The best solutions thoughtfully combine sufficient depth, restrictive openings, and smart placement to maintain public sanitation and safety without making legitimate disposal a chore for the public.