  We consider the coloring of certain distance graphs on the Euclidean plane.
Namely, we ask for the minimal number of colors needed to color all points of
the plane in such a way that pairs of points at distance in the interval
$[1,b]$ get different colors. The classic Hadwiger-Nelson problem is a special
case of this question -- obtained by taking $b=1$. The main results of the
paper are improved lower and upper bounds on the number of colors for some
values of $b$. In particular, we determine the minimal number of colors for two
ranges of values of $b$ - one of which is enlarging an interval presented by
Exoo and the second is completely new. Up to our knowledge, these are the only
known families of distance graphs on the plane with a determined nontrivial
chromatic number. Moreover, we present the first $8$-coloring for $b$ larger
than values of $b$ for the known $7$-colorings. As a byproduct, we give some
bounds and exact values for bounded parts of the plane, specifically by
coloring certain annuli.
