Consider a 20 cm long cylindrical glass of refractive index n=2.0. Left end of it is a concave spherical mirror with
radius of curvature 12 cm for an object O inside the cylinder. The shape of the right end of the cylindrical glass is not
known. If the object is at 10 cm to the right of the mirrored surface, an outside observer looking from right sees the final
image I at 5 cm to the left of the right surface.
a) Find the shape of this surface. Is it concave or convex (if so, calculate the radius of curvature) or plane, with respect to
an outside observer?
b) Calculate the total magnification, and describe the final image.
(Note that, in this problem rays reaching to the unknown surface directly from the object will not be considered.)