A transparent thin film of uniform thickness and refractive index $$n_1 = 1.4$$ is coated on the convex spherical surface of radius Rat one end of a long solid glass cylinder of refractive index $$n_2 = 1.5,$$ as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance $$f_1$$ from the film, while rays of light traversing from glass to air get focused at distance $$f_2$$ from the film. Then