  Rayleigh scattering has shown powerful abilities to study electron resonances
of nanomaterials regardless of the specific shapes. In analogy to Rayleigh
scattering, here we demonstrate that edge optical scattering from
two-dimensional (2D) materials also has the similar advantage. Our result shows
that, in visible spectral range, as long as the lateral size of a 2D sample is
larger than 2 {\mu}m, its edge scattering is essentially a knife-edge
diffraction, and the intensity distribution of the high-angle scattering in
$\mathbf{k}$ space is nearly independent of the lateral size and the shape of
the 2D samples. The high-angle edge scattering spectra are purely determined by
the intrinsic dielectric properties of the 2D materials. As an example, we
experimentally verify this feature in single-layer $MoS_{2}$, in which A and B
excitons are clearly detected in the edge scattering spectra, and the
scattering images in $\mathbf{k}$ space and real space are consistent with our
theoretical model. This study shows that the edge scattering is a highly
practical and efficient method for optical studies of various 2D materials as
well as thin films with clear edges.
