In short, it depends on where they enter the ocean and how buoyant/resilient the material is.
If the sunglasses are buoyant (i.e. they stay at the sea-surface) and avoid being smashed up by waves or degraded by sunlight, then where they end up with largely depend on large-scale ocean currents. This is a very complicated subject but there are certain current systems in the ocean called [subtropical gyres](https://en.wikipedia.org/wiki/Ocean_gyre#Subtropical_gyres) that tend to accumulate things floating at the surface. You may have heard of the [Great Pacific Garbage Patch](https://en.wikipedia.org/wiki/Great_Pacific_garbage_patch) and this is exactly what has led to the accumulation of trash in this region, but similar things exist in the other ocean basins. There is absolutely no guarantee that buoyant trash in the ocean will end up trapped in one of these gyres (how likely depends on where it entered the ocean) but they are zones of accumulation. Even if sunglasses enter one of these systems, waves and sunlight will eventually cause them to break down into smaller fragments (possibly microplastics eventually) and ultimately sink to the ocean floor.
On the other hand, if the sunglasses are not buoyant then they will make their way to the sea floor before they enter one of these large current systems. If they never make it far out to sea then they will rapidly get fragmented by waves near the shore. If they do make it some distance out to sea before reaching the sea floor then they may reach the calmer sea floor intact.
Once the sunglasses are at the sea floor, they’re probably not going to move around much, particularly if they’ve managed to avoid being smashed up. Currents at the sea floor are generally much, much weaker than currents at the surface, although [recently some research](https://science.sciencemag.org/content/368/6495/1140) has suggested that deep ocean currents could be important for redistributing microplastics.
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