This paper is initiated by the article [1], where mathematical technique of short wave diffraction by a convex prolate body is being applied to the plane wave diffraction by a thin cone with small angle at the apex. The wave field is studied there under condition $kz\gg1$, where $k$ is the wave number and $z$ is the distance to the apex, therefore the wave generated by the apex can hardly be involved into consideration. For description of the two rest waves, the incident and reflected ones, it seems natural to make use of the ray method. In this paper, two terms of ray series are constructed and validity condition of ray method is deduced. Obtained formulae have explicit form and do not contain any special functions.