(Originais Teachy 2023) - Question Very Hard of Physics

A concave mirror of a telescope has a radius of curvature of 2 meters. A small lamp is placed 6 meters from the mirror, along the principal axis. Determine the distance and position of the image formed by the lamp, considering the characteristics of concave mirrors. Use the mirror equation and Gauss formula to solve the problem, where 'p' is the distance from the object to the mirror, 'f' is the focal length of the mirror, and 'q' is the distance from the image to the mirror. Consider that the lamp is a small object and that the light rays approach the principal axis. Explain the meaning of the signs in the equation and how they relate to the formation of the image. Additionally, discuss the quality of the image formed in terms of sharpness and size in relation to the position of the lamp and the focal length of the mirror.