1. A dot sighting device comprising: a reflection mirror; an illumination having a LED irradiating light to the reflection mirror and a transparent reticle that is positioned in front of the LED and forms a dot image by transmitting the light irradiated from the LED; a fixed grille formed on a lower portion of the dot sighting device; wherein the dot sighting device is attached to and detached from a mount for a heavy machine gun by the fixed grille: wherein the reflection mirror comprises a doublet, with a first surface, an interior second surface and a third surface, with the first surface and third surface being spherical, wherein the interior second surface of the reflection mirror comprises a LED reflection surface; wherein a radius curvature of the first and third surfaces satisfies the following equation: D 1 = n - 1 R 1 , D 2 = 1 - n R 3 ( 1 ) D 1 + D 2 - d n ⁢ D 1 ⁢ D 2 = 0 wherein D 1 denotes a refractive power of the first surface D 2 denotes a refractive power of the third surface, d denotes a distance between the centers of the first and third surfaces, R 1 denotes a radius curvature of the first surface, R 3 denotes a radius curvature of the third surface, and n denotes a refractive index of the material.