The Huygens eyepiece follows the principle of minimizing spherical aberration by arranging two plano-convex lenses with their curved surfaces facing each other. An analysis reveals that chromatic aberration is minimised for the Huygens eyepiece when the spacing between the lenses, denoted as L, equals half the sum of their focal lengths L = 1/2(f1 + f2). Let's shift our focus to the design of a Huygens eyepiece, aiming to achieve a 12x magnification. Given that the first lens of the Smithson eyepiece has a focal length of 35 mm, calculate the following:
(i) The focal length of the second lens in the Huygens eyepiece.
(ii) The spacing between the first and second lenses in the Huygens eyepiece.