$(20$ points$)$ Briefly answer the following conceptual questions:

$($a$)(5$ points$)$ Describe what the young lady from the painting $"$An Evening Out" by the Spanish artist Raimundo de Madrazo y Garreta sees when she holds a small mirror in front of herself while her back is leaning against a large plane mirror.

$($b$)(5$ points$)$ A point source and two of its images produced by two plane mirrors are at the vertices of an equilateral triangle. Describe where the mirrors are located and what is the angle between them.

$($c$)(5$ points$)$ Legend has it that Archimedes, acting as an advisor to the ruler of Syracuse, devised an optical system made of shields that could concentrate sunlight sufficiently well to set enemy boats on fire from a distance. How plausible is this legend? Explain carefully using what you know about spherical mirrors.

$($d$)(5$ points$)$ Is every double convex thin lens converging? If yes, explain why. If not, provide a counter example.