1. The problem statement, all variables and given/known data A person's eye has a near point of 7 cm. The cornea at the outer surface of the eye has a refractive index of n_c = 1.376 and forms a convex shape with a radius of curvature of R_2 = 8 mm against air. The figure below shows the same eye with a contact lens (refractive index of n_L = 1.5) mounted against the cornea such that second (right) surface matches the curvature of the cornea (i.e. R_2= 8 mm). Determine the radius R_1 of the first surface of the contact lens that will correct the near point to the normal 25 cm distance from the eye. Assume paraxial and thin lens conditions. 2. Relevant equations (1) 1/f =1/f_1 + 1/f_2, (2) 1/f_1 = (n/c -1) (1/R_1 -1/R_2), (3) 1/f_2 = (n_L -1)(1/R_2), (4) 1/u + 1/v = 1/f 3. The attempt at a solution The focal length of the combined lenses required to correct the present myopia is found from the Gaussian thin lens equation as 1/-7 + 1/-25 = 1/f ⇒ f= -5.47. Using paraxial optics and Fermat's principle of least time relevant equations (1)-(3) are easily found by requiring that all paths through the lens take equal time to reach the focus. Substituting (2) and (3) into (1) with the given numbers we find R_1 =-17.98 cm.