Adjust binwidth size for faceted dotplot with free y axis

Question

I would like to adjust the binwidth of a faceted geom_dotplot while keeping the dot sizes the same.

Using the default binwidth (1/30 of the data range), I get the following plot:

library(ggplot2)

df = data.frame(
  t = c(1, 1, 1, 1, 1, 2, 2, 2, 2, 2),
  x = 1, 
  y = c(1, 2, 3, 4, 5, 100, 200, 300, 400, 500)
)

ggplot(df, aes(x=x, y=y)) +
  geom_dotplot(binaxis="y", stackdir="center") +
  facet_wrap(~t, scales="free_y")

However, if I change the binwidth value, the new value is taken as an absolute value (and not the ratio of the data range), so the two facets get differently sized dots:

  geom_dotplot(binaxis="y", stackdir="center", binwidth=2) +

Is there a way to adjust binwidth so it is relative to its facet's data range?