(Originais Teachy 2023) - Question Medium of Physics

A converging spherical glass lens with a refractive index of 1.5 and a radius of curvature of 20 cm (half for each surface) is immersed in an unknown liquid, forming a high-precision optical system. An observer positioned in the air, in the same direction as the lens's principal axis, observes that an object is formed at the lens's position, projecting a sharp image at 60 cm from the lens. Considering that the lens is 'thin', meaning the distance between the lens surfaces is disregarded, determine: (1) The focal distance of the lens in the unknown liquid. (2) If the lens is submerged in a liquid with a refractive index of 1.8, what would be the new focal distance? Disregard the lens thickness and use the lens maker's equation: 1/f = (n_lens - n_air)/(n_air * (1/R1 - 1/R2)), where f is the focal distance, n_lens is the lens refractive index, n_air is the air refractive index, and R1 and R2 are the curvature radii of the lens surfaces. For 'thin' lenses, we consider that R1 and R2 have opposite signs and the focal distance is positive for converging lenses.