  The paper studies intrinsic geometry in the tropical plane. Tropical
structure in the real affine $n$-space is determined by the integer tangent
vectors. Tropical isomorphisms are affine transformations preserving the
integer lattice of the tangent space, they may be identified with the group
$\operatorname{GL_n}(\mathbb{Z})$ extended by arbitrary real translations. This
geometric structure allows one to define wave front propagation for boundaries
of convex domains. Interestingly enough, an arbitrary compact convex domain in
the tropical plane evolves to a finite polygon after an arbitrarily small time.
The caustic of a wave front evolution is a tropical analytic curve. The paper
studies geometry of the tropical wave fronts and caustics. In particular, we
relate the caustic of a tropical angle to the continued fraction expression of
its slope, and treat it as a tropical trigonometry notion.
